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Systematic studies on the profile and behavior of solutions of partial differential equations

Research Project

Project/Area Number 24244012
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

Yanagida Fiji  東京工業大学, 理学院, 教授 (80174548)

Co-Investigator(Kenkyū-buntansha) 仙葉 隆  福岡大学, 理学部, 教授 (30196985)
内藤 雄基  愛媛大学, 理工学研究科(理学系), 教授 (10231458)
壁谷 喜継  大阪府立大学, 工学(系)研究科(研究院), 教授 (70252757)
石渡 通徳  大阪大学, 基礎工学研究科, 教授 (30350458)
高坂 良史  神戸大学, 海事科学研究科, 准教授 (00360967)
谷口 雅治  岡山大学, 自然科学研究科, 教授 (30260623)
Research Collaborator Polacik Peter  University of Minnesota, School of Mathematics, Professor
Fila Marek  Comenius University, Department of Applied Mathematics and Statistics, Professor
Shi Jun-Ping  College of William and Mary, Mathematics, Professor
Htoo Khin Phyu Phyu  Mandalay University, Department of Mathematics, Lecturer
Hui Kin-Ming  Academia Sinica, Institute of Mathematics, Research Fellow(Professor)
Chern Jann-Long  National Central University, Department of Mathematics, Professor
Chen Chiun-Chuan  National Taiwan University, Department of Mathematics, Professor
Marta Garcia-Huidobro  Pontificia Universidad Catálica de Chile, Facultad de Mathemóticas, Professor
Lou Yuan  Ohio States University, Deaprtment of Mathematics, Professor
Project Period (FY) 2012-05-31 – 2017-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥44,720,000 (Direct Cost: ¥34,400,000、Indirect Cost: ¥10,320,000)
Fiscal Year 2016: ¥9,490,000 (Direct Cost: ¥7,300,000、Indirect Cost: ¥2,190,000)
Fiscal Year 2015: ¥9,230,000 (Direct Cost: ¥7,100,000、Indirect Cost: ¥2,130,000)
Fiscal Year 2014: ¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000)
Fiscal Year 2013: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2012: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Keywords形状解析 / 漸近挙動 / 安定性 / 特異性 / 進行波解 / 解の爆発 / 関数方程式 / 解析学 / 楕円型方程式 / 熱方程式 / 走化性方程式 / 関数方程式の大域理論 / 分岐構造
Outline of Final Research Achievements

We carried out systematic studies on the profile and behavior of solutions of elliptic and parabolic partial differential equations, and obtained the following results among others.
For elliptic equations, we showed a Liouville-type theorem for an equation transformed by a scaling method. We also obtained results on the existence and no-existence of singular solutions and the structure of positive solutions for equations on the sphere, and equations with space-dependent exponent of nonlinearities.
For parabolic equations, we made clear the structure of solutions of a linear heat equation with inverse-square potential. We also studied the Fujita equation about the boundedness of time-global solutions, existence of singular solutions and their stability, and Fisher's equation about the dynamics of interfaces.

Report

(6 results)
  • 2017 Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (189 results)

All 2017 2016 2015 2014 2013 2012 Other

All Int'l Joint Research (5 results) Journal Article (59 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 55 results,  Open Access: 13 results,  Acknowledgement Compliant: 11 results) Presentation (121 results) (of which Int'l Joint Research: 25 results,  Invited: 104 results) Book (1 results) Funded Workshop (3 results)

  • [Int'l Joint Research] ミネソタ大学/オハイオ州立大学(米国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] コメニウス大学(スロバキア)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] マンダレー大学(ミャンマー)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Academia Sinica, Taiwan(台湾)

    • Related Report
      2014 Annual Research Report
  • [Int'l Joint Research] コメニウス大学(スロバキア)

    • Related Report
      2014 Annual Research Report
  • [Journal Article] Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity.2017

    • Author(s)
      Kentarou Fujie, Takasi Senba
    • Journal Title

      Nonlinearity

      Volume: 29 Issue: 8 Pages: 2417-2450

    • DOI

      10.1088/0951-7715/29/8/2417

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A priori bounds for superlinear elliptic equations with semidefinite nonlinearity2017

    • Author(s)
      Yuki Naito, Takashi Suzuki, Yohei Toyota
    • Journal Title

      Nonlinear Anal.

      Volume: 151 Pages: 18-40

    • DOI

      10.1016/j.na.2016.11.016

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The heat kernel of a Schroedinger operator with inverse square potential2017

    • Author(s)
      K. Ishige, Y. Kabeya, E. Ouhabaz
    • Journal Title

      Proceedings of the London Mathematical Society

      Volume: 115 Issue: 2 Pages: 381-410

    • DOI

      10.1112/plms.12041

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Hardy type inequalities in $L_p$ with sharp remainders2017

    • Author(s)
      N. Ioku, M. Ishiwata, T. Ozawa
    • Journal Title

      Journal of Inequalities and Applications

      Volume: - Issue: 1 Pages: 1-7

    • DOI

      10.1186/s13660-016-1271-1

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Convergence rate to singular steady states in a semilinear parabolic equation2016

    • Author(s)
      M. Hoshino and E. Yanagida
    • Journal Title

      Nonlinear Analysis

      Volume: 131 Pages: 98-111

    • DOI

      10.1016/j.na.2015.06.020

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Time-dependent singularities in a semilinear parabolic equation with absorption2016

    • Author(s)
      Jin Takahashi, Eiji Yanagida
    • Journal Title

      Communications in Contemporary Mathematics

      Volume: 印刷中 Issue: 05 Pages: 1550077-1550077

    • DOI

      10.1142/s0219199715500777

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Singular solutions of the scalar field equation with a critical exponent2016

    • Author(s)
      J.-L. Chern and E. Yanagida
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 176 Pages: 277-288

    • DOI

      10.1007/978-3-319-41538-3_16

    • ISBN
      9783319415369, 9783319415383
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On the effect of equivalent constraints on a maximizing problem associated with the Sobolev type embeddings in R^N2016

    • Author(s)
      Michinori Ishiwata, Hidemitsu Wadade
    • Journal Title

      Mathematische Annalen

      Volume: 364 Issue: 3-4 Pages: 1043-1068

    • DOI

      10.1007/s00208-015-1243-7

    • NAID

      120005652940

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation2016

    • Author(s)
      Yoshihito Kohsaka
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 176 Pages: 121-148

    • DOI

      10.1007/978-3-319-41538-3_8

    • ISBN
      9783319415369, 9783319415383
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivitiy2016

    • Author(s)
      K. Fujie and T. Senba
    • Journal Title

      Discrete and Continuous Dynamical Systems - Series B

      Volume: 21 Issue: 1 Pages: 81-102

    • DOI

      10.3934/dcdsb.2016.21.81

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Singular solutions to a nonlinear elliptic equation on the whole unit sphere2016

    • Author(s)
      S. Bae, J.-L. Chern, Y. Kabeya and S. Yotsutani
    • Journal Title

      RIMS Kokyuroku

      Volume: -

    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Sharp remainder of a critical Hardy inequality2015

    • Author(s)
      N. Ioku, M. Ishiwata, T. Ozawa
    • Journal Title

      Archiv der Mathematik

      Volume: 106 Issue: 1 Pages: 65-71

    • DOI

      10.1007/s00013-015-0841-7

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Instability of multi-spot patterns in shadow systems of reaction-diffusion equations2015

    • Author(s)
      S.-I. Ei, K. Ikeda and E. Yanagida
    • Journal Title

      Commun. Pure Appl. Anal.

      Volume: 14 Issue: 2 Pages: 717-736

    • DOI

      10.3934/cpaa.2015.14.717

    • NAID

      120005732975

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Time-dependent singularities in the heat equation2015

    • Author(s)
      J. Takahashi and E. Yanagida
    • Journal Title

      Commun. Pure Appl. Anal.

      Volume: 14 Issue: 3 Pages: 969-979

    • DOI

      10.3934/cpaa.2015.14.969

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Sharp decay estimates in Lorentz spaces for nonnegative Schrodinger heat semigroups2015

    • Author(s)
      Norisuke Ioku, K. Ishige and E. Yanagida
    • Journal Title

      J. Math. Pures Appl.

      Volume: 103(4) Issue: 4 Pages: 900-923

    • DOI

      10.1016/j.matpur.2014.09.006

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Global attractivity and convergence rate in the weighted norm for a supercritical semilinear heat equation2015

    • Author(s)
      Yuki Naito
    • Journal Title

      Differential Integral Equations

      Volume: 28

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solutions to the equation of the scalar-field type on a large spherical cap2015

    • Author(s)
      Y. Kabeya
    • Journal Title

      RIMS Kokyuroku

      Volume: 1974

    • Related Report
      2015 Annual Research Report
    • Open Access
  • [Journal Article] On a variational problem associated with a Hardy type inequality involving a mean oscillation2015

    • Author(s)
      N. Ioku, and M. Ishiwata
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: 54 Issue: 4 Pages: 3949-3966

    • DOI

      10.1007/s00526-015-0927-x

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A scale invariant form of a critical Hardy inequality2015

    • Author(s)
      N. Ioku, and M. Ishiwata
    • Journal Title

      Int. Math. Res. Not. IMRN

      Volume: 2015 Issue: 18 Pages: 8830-8846

    • DOI

      10.1093/imrn/rnu212

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the sharp constant of the weighted Trudinger-Moser type inequality and an application to nonlinear Klein-Gordon equations2015

    • Author(s)
      M. Ishiwata, M. Nakamura, H. Wadade
    • Journal Title

      Discrete and Continuous Dynamical System - A

      Volume: 35 Issue: 10 Pages: 4889-4903

    • DOI

      10.3934/dcds.2015.35.4889

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 表面拡散方程式と平均曲率一定曲面2015

    • Author(s)
      高坂良史
    • Journal Title

      数理解析研究所講究録

      Volume: 1979

    • Related Report
      2015 Annual Research Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] Non-accessible singular homoclinic orbits for a semilinear parabolic equation2014

    • Author(s)
      M. Fila and E. Yanagida
    • Journal Title

      Differential Integral Equations

      Volume: 27

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Global unbounded solutions of the Fujita equation in the intermediate range2014

    • Author(s)
      Peter Polacik and Eiji Yanagida
    • Journal Title

      Math. Ann.

      Volume: 360 Issue: 1-2 Pages: 255-266

    • DOI

      10.1007/s00208-014-1038-2

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics2014

    • Author(s)
      Peter Polacik and Eiji Yanagida
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 46-5 Issue: 5 Pages: 3481-3496

    • DOI

      10.1137/140958566

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a weak attractor of a class of PDEs with degenerate diffusion and chemotaxis2014

    • Author(s)
      Messoud Efendiev, Takasi Senba, Anna Zhigun
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 66 Issue: 4 Pages: 1133-1153

    • DOI

      10.2969/jmsj/06641133

    • NAID

      130004705997

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Convergence rate in the weighted norm for a semilinear heat equation with supercritical nonlinearity2014

    • Author(s)
      Yuki Naito
    • Journal Title

      Kodai Mathematical Journal

      Volume: 37 Issue: 3 Pages: 646-667

    • DOI

      10.2996/kmj/1414674614

    • NAID

      130004705917

    • ISSN
      0386-5991, 1881-5472
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Existence and separation of positive radial solutions for semilinear elliptic equations2014

    • Author(s)
      Soohyun Bae, Yuki Naito
    • Journal Title

      J. Differential Equations

      Volume: 257 Issue: 7 Pages: 2430-2463

    • DOI

      10.1016/j.jde.2014.05.042

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A remark on self-similar solutions for a semilinear heat equation with critical Sobolev exponent2014

    • Author(s)
      Yuki Naito
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 64

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Eigenvalues of the Laplace-Beltrami operator on a large spherical cap under the Robin problem2014

    • Author(s)
      Yoshitsugu Kabeya, Tatsuki Kawakami, Atsushi Kosaka, Hirokazu Ninomiya
    • Journal Title

      Kodai Mathematical Journal

      Volume: 37 Issue: 3 Pages: 620-645

    • DOI

      10.2996/kmj/1414674613

    • NAID

      130004705916

    • ISSN
      0386-5991, 1881-5472
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the sharp constant for the weighted Trudinger-Moser type inequality of the scaling invariant form2014

    • Author(s)
      M. Ishiwata, M. Nakamura, and H. Wadade
    • Journal Title

      Ann. Inst. H. Poincare Anal. Non Lineaire

      Volume: 31 Issue: 2 Pages: 297-314

    • DOI

      10.1016/j.anihpc.2013.03.004

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems2014

    • Author(s)
      Y.-Y. Chen, Y. Kohsaka and H. Ninomiya
    • Journal Title

      Discrete and continuous dynamical systems. Ser. B

      Volume: 19 Issue: 3 Pages: 697-714

    • DOI

      10.3934/dcdsb.2014.19.697

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space2014

    • Author(s)
      Yen-Lin Wu, Chi-You Chen, Jann-Long Chern, Yoshitsugu Kabeya
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 13 Issue: 2 Pages: 949-960

    • DOI

      10.3934/cpaa.2014.13.949

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mean curvature flow with triple junctions in higher space dimensions2014

    • Author(s)
      Daniel Depner, Harald Garcke, Yoshihito Kohsaka
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: 211 Issue: 1 Pages: 301-334

    • DOI

      10.1007/s00205-013-0668-y

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence and blow-up of solutions for a complex-valued heat equation with a quadratic nonlinearity2013

    • Author(s)
      Jong-Shenq Guo, Hirokazu Ninomiya, Masahiko Shimojo and Eiji Yanagida
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 365 Issue: 5 Pages: 2447-2467

    • DOI

      10.1090/s0002-9947-2012-05797-7

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Behavior of global solutions of the Fujita equation2013

    • Author(s)
      E. Yanagida
    • Journal Title

      Sugaku Expositions

      Volume: 26 Pages: 129-147

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sharp decay estimates of L^q norms of nonnegative Schroedinger heat semigroups2013

    • Author(s)
      Norisuke Ioku, Kazuhiro Ishige and Eiji Yanagida
    • Journal Title

      J. Funct. Anal.

      Volume: 264 Issue: 12 Pages: 2764-2783

    • DOI

      10.1016/j.jfa.2013.03.009

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of stationary solutions and existence of oscillationg solutions to a chemotaxis system in high dimensional spaces2013

    • Author(s)
      Takasi Senba
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 56 Pages: 339-378

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the behavior of radial solutions to a parabolic-elliptic system related to biology2013

    • Author(s)
      仙葉隆(Takasi Senba)
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1856 Pages: 143-151

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Characterization for rectifiable and nonrectifiable attractivity of nonautonomous systems of linear differential equations2013

    • Author(s)
      Yuki Naito, Mervan Pasic,
    • Journal Title

      Int. J. Differ. Equ.

      Volume: Art ID 740980 Pages: 1-11

    • DOI

      10.1155/2013/740980

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fractal oscillations near the domain boundary of radially symmetric solutions of p-Laplace equations2013

    • Author(s)
      Yuki Naito, Mervan Pasic, Satoshi Tanaka and Darko Zubrinic,
    • Journal Title

      Contempt Math.

      Volume: 601 Pages: 325-343

    • DOI

      10.1090/conm/601/11912

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A unified approach to Matukuma type equations on the hyperbolic space or on a sphere2013

    • Author(s)
      Yoshitsugu Kabeya
    • Journal Title

      Discrete and Continuous Dynamical Systems, Supplement

      Volume: 1 Pages: 385-391

    • DOI

      10.3934/proc.2013.2013.385

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the existence and nonexistence of maximizers associated with Trudinger-Moser type inequalities in unbounded domains2013

    • Author(s)
      Michinori Ishiwata
    • Journal Title

      Emerging topics on differential equations and their applications, Nankai series in pure, applied mathematics and theoretical physics

      Volume: 10 Pages: 41-53

    • DOI

      10.1142/9789814449755_0004

    • ISBN
      9789814449748, 9789814449755
    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Positive solution to semilinear parabolic equation associated with critical Sobolev exponent2013

    • Author(s)
      M. Ishiwata, and T. Suzuki
    • Journal Title

      NoDEA Nonlinear Differential Equations Appl.

      Volume: 20 Issue: 4 Pages: 1553-1576

    • DOI

      10.1007/s00030-013-0221-6

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiple positive solutions of semilinear elliptic equations with weight function in exterior domains2013

    • Author(s)
      Michinori Ishiwata
    • Journal Title

      Differential and Integral Equations

      Volume: 26 Pages: 183-200

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bounded and unbounded oscillating solutions to a parabolic-elliptic system in two dimensional2013

    • Author(s)
      Yuki Naito, Takasi Senba.
    • Journal Title

      Communications on Pure Applied Analysis

      Volume: 12 Issue: 5 Pages: 1861-1880

    • DOI

      10.3934/cpaa.2013.12.1861

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay rate of L^q norms of critical schrodinger heat semigroups2013

    • Author(s)
      K. Ishige and Y. Kabeya
    • Journal Title

      ``Geometric Properties for Parabolic and Elliptic PDE's", in Springer INdAM Series

      Volume: 2 Pages: 165-178

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations2013

    • Author(s)
      Yong Jung Kim, Wei-Ming Ni and Masaharu Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: Vol. 33, No 8 Issue: 8 Pages: 3707-3718

    • DOI

      10.3934/dcds.2013.33.3707

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traveling fronts of pyramidal shapes in competition-diffusion systems2013

    • Author(s)
      Wei-Ming Ni and Masaharu Taniguchi
    • Journal Title

      Networks and Heterogeneous Media

      Volume: Vol. 8, No. 1 Issue: 1 Pages: 379-395

    • DOI

      10.3934/nhm.2013.8.379

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Appearance of anomalous singularities in a semilinear parabolic equation, Commun2012

    • Author(s)
      S. Sato and E. Yanagida
    • Journal Title

      Pure Appl. Anal. 11

      Volume: no.1 Issue: 1 Pages: 387-405

    • DOI

      10.3934/cpaa.2012.11.387

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation2012

    • Author(s)
      M. Fila, J. L. Vazquez, M. Winkler and E. Yanagida
    • Journal Title

      Arch. Rational Mech. Anal.

      Volume: 204 Issue: 2 Pages: 599-625

    • DOI

      10.1007/s00205-011-0486-z

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Solution to an Ambarzumyan Problem on Trees2012

    • Author(s)
      C.-K. Law and E. Yanagida
    • Journal Title

      Kodai Math. J.

      Volume: 35 Pages: 358-373

    • NAID

      130004496167

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blow-up behavior of solutions to a parabolic-elliptic system on higher dimensional domains2012

    • Author(s)
      Y. Naito
    • Journal Title

      Discrete and Continuous Dynamical System - A

      Volume: 32 Issue: 10 Pages: 3691-3713

    • DOI

      10.3934/dcds.2012.32.3691

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations2012

    • Author(s)
      Yuki Naito
    • Journal Title

      J. Differential Equations

      Volume: 253 Issue: 11 Pages: 3029-3060

    • DOI

      10.1016/j.jde.2012.08.013

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on singular Sturm comparison theorems2012

    • Author(s)
      Yuki Naito
    • Journal Title

      Mem. Differential Equations Math. Phys.

      Volume: 57 Pages: 109-122

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of second order linear differential equations and an application to singular elliptic eigenvalue problems2012

    • Author(s)
      Y.Naito
    • Journal Title

      Bull.London Math.Soc.

      Volume: (In press) Issue: 3 Pages: 1-18

    • DOI

      10.1112/blms/bdr117

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent2012

    • Author(s)
      Yuki Naito and Tokushi Sato
    • Journal Title

      Ann. Mat. Pura Appl. (4)

      Volume: 191 Issue: 1 Pages: 25-51

    • DOI

      10.1007/s10231-010-0173-y

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rectifiable oscillations of radially symmetric solutions of p-Laplace differential equations2012

    • Author(s)
      Yuki Naito, Mervan Pasic, and Hiroyuki Usami
    • Journal Title

      Differ. Equ. Appl.

      Volume: 4 Issue: 1 Pages: 11-25

    • DOI

      10.7153/dea-04-03

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heat equation with a singular potential on the boundary and the Kato inequality2012

    • Author(s)
      K. Ishige and M. Ishiwata
    • Journal Title

      J. Anal. Math.

      Volume: 118 Issue: 1 Pages: 161-176

    • DOI

      10.1007/s11854-012-0032-4

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global solutions for a semilinear heat equation in the exterior domain of a compact set2012

    • Author(s)
      K. Ishige and M. Ishiwata
    • Journal Title

      Discrete Contin. Dyn. Syst.

      Volume: 32 Issue: 3 Pages: 847-866

    • DOI

      10.3934/dcds.2012.32.847

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Extinction of solutions of the logarithmic diffusion equation2017

    • Author(s)
      柳田英二
    • Organizer
      第34回九州における偏微分方程式研究集会
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Long-time behavior of solutions of the Fisher-KPP equation for slowly decaying initial data2017

    • Author(s)
      Eiji Yanagida
    • Organizer
      Mathematical Analysis on Nonlinear PDEs
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Separation structure of solutions for elliptic equations with exponential nonlinearity2017

    • Author(s)
      Yuki Naito
    • Organizer
      2017 International Workshop on Nonlinear PDE and Applications
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Incomplete blow-up of solutions for semilinear heat equations with supercritical nonlinearity2017

    • Author(s)
      内藤雄基
    • Organizer
      研究集会「第34回九州における偏微分方程式研究集会」
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Asymptotic self-similarity of solutions to semilinear heat equations2017

    • Author(s)
      内藤雄基
    • Organizer
      研究集会「Mathematical Analysis on Nonlinear PDEs」
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Positive Schrodinger operators with the inverse square potential and related topics2017

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      南大阪応用数学セミナー
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Positive Schrodinger operators with the inverse square potential and related topics2017

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      Mathematical Analysis on Nonlinear PDEs
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the bifurcation diagrams for steady states of the surface diffusion equation2017

    • Author(s)
      高坂良史
    • Organizer
      International Conference on PDEs, Geometric Analysis and Functional Inequalities
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 表面拡散方程式の定常問題としての Delaunay 曲面の安定性解析2017

    • Author(s)
      高坂良史
    • Organizer
      大阪駅前セミナー
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式の定常解の安定性解析について2016

    • Author(s)
      高坂良史
    • Organizer
      Geometric flows and related problems
    • Place of Presentation
      東京工業大学 (東京都目黒区)
    • Year and Date
      2016-03-03
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of the steady states for the surface diffusion equation2016

    • Author(s)
      高坂良史
    • Organizer
      松山解析セミナー2016
    • Place of Presentation
      愛媛大学 (愛媛県松山市)
    • Year and Date
      2016-02-05
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the variational problem associated with the Trudinger-Moser and the Sobolev type inequalities2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      The 33rd Kyushu Symposium on Partial Differential Equations
    • Place of Presentation
      Kyushu University, Nishijin Plaza(福岡市早良区)
    • Year and Date
      2016-01-29
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Extinction profile of solutions of the logarithmic diffusion equation on R2016

    • Author(s)
      柳田英二
    • Organizer
      RIMS 研究集会『偏微分方程式の解の形状解析』
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Boundary singularity in a semilinear parabolic equation with the Neumann boundary conditions2016

    • Author(s)
      Eiji Yanagida
    • Organizer
      7th Euro-Japanese Workshop on Blow-up
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Removable and non-removable singularities in some parabolic equations2016

    • Author(s)
      Eiji Yanagida
    • Organizer
      The 7th Pacific RIM Conference on Mathematics 2016
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamics of solutions the Fisher -KPP equation for slowly decaying initial data2016

    • Author(s)
      Eiji Yanagida
    • Organizer
      International Conference on Reaction-Diffusion Equations and Their Applications to the Life, Social and Physical Sciences
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Global existence and boundedness of solutions to chemotaxis systems with general sensitivity2016

    • Author(s)
      Takasi Senba
    • Organizer
      7th Euro-Japanese Workshop on Blow-up
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Singular extremal solutions for supercritical elliptic equations in a ball2016

    • Author(s)
      内藤雄基
    • Organizer
      常微分方程式の定性的理論ワークショップ
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] A priori bounds for superlinear ellitptic equations with semidefinite nonlinearity2016

    • Author(s)
      鈴木貴、豊田洋平、内藤雄基
    • Organizer
      日本数学会秋季大会
    • Related Report
      2016 Annual Research Report
  • [Presentation] Peaking solutions to semilinear heat equations with supercritical nonlinearities2016

    • Author(s)
      Yuki Naito
    • Organizer
      7th Euro-Japanese Workshop on Blow-up
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of bifurcation diagrams for supercritical elliptic equations in a ball2016

    • Author(s)
      内藤雄基
    • Organizer
      第141回神楽坂解析セミナー
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Difference equation and the related Schrodinger operator2016

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      The 22nd International Conference on Difference Equations and Applications
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the compactness of the embedding $H_0^1(\OMega)\hookrightarrow L^{q(x)}(\Omega)$2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      International Workshop on Nonlinear PDEs 2016 in Osaka
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the compactness of the Sobolev type embedding with variable exponent2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      熊本大学応用解析セミナー
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 非コンパクトな軌道を持つ力学系を巡って2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      愛媛大学数学教室談話会
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] ゼータ正規化された経路積分と熱方程式の基本解について2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      グラフゼータと量子ウォークの諸相(室蘭工業大学)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] A remark on the compactness of the Sobolev type embedding with variable exponent2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      Pacific Rim Conference
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On the compactness of the Sobolev embedding with a variable exponent2016

    • Author(s)
      Michinori Ishiwata
    • Organizer
      信州大学偏微分方程式研究集会
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Bifurcation analysis for steady states of surface diffusion equation2016

    • Author(s)
      高坂良史
    • Organizer
      Elucidation of configurational structure in micro behavior and collective pattern formation
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式の定常曲面の安定性について2016

    • Author(s)
      高坂良史
    • Organizer
      東北大学応用数学セミナー
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of steady states for surface diffusion equation2016

    • Author(s)
      高坂良史
    • Organizer
      Workshop on nonlinear partial differential equations and related topics
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Stability of Delaunay surfaces as the steady states for the surface diffusion equation2015

    • Author(s)
      高坂良史
    • Organizer
      Geometric aspects on capillary problems and related topics
    • Place of Presentation
      Instituto de Matematicas (IEMath), Granada, Spain
    • Year and Date
      2015-12-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Structure of positive solutions for semilinear elliptic equations with supercritical growth2015

    • Author(s)
      内藤雄基
    • Organizer
      第5回弘前非線形方程式研究会
    • Place of Presentation
      弘前大学理工学部(青森県弘前市)
    • Year and Date
      2015-12-12
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 体積保存性をもつ曲面の発展方程式の定常曲面の安定性について2015

    • Author(s)
      高坂良史
    • Organizer
      MPM2015
    • Place of Presentation
      宮崎大学 (宮崎県宮崎市)
    • Year and Date
      2015-11-13
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Structure of positive solutions for semilinear elliptic equations with supercritical growth2015

    • Author(s)
      内藤雄基
    • Organizer
      RIMS 研究集会「偏微分方程式の解の形状と諸性質」
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-11-11
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Singular solutions to a nonlinear elliptic equation on the whole unit sphere2015

    • Author(s)
      Y. Kabeya
    • Organizer
      RIMS Workshop on Qualitative theory of ordinary differential equations in real domains
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-11-11
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 非線形知覚関数を持つ走化性方程式系の解の挙動について2015

    • Author(s)
      仙葉隆
    • Organizer
      RIMS研究集会「非線形現象の解析への応用としての発展方程式論の展開」
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-10-21
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Global attractivity in the weighted norm for a supercritical semilinear heat equation2015

    • Author(s)
      内藤雄基
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      京都産業大学(京都市北区)
    • Year and Date
      2015-09-05
    • Related Report
      2015 Annual Research Report
  • [Presentation] Analysis of stability of the CMC surfaces via the surface diffusion equation2015

    • Author(s)
      高坂良史
    • Organizer
      Summer School on multiscale and geometric analysis
    • Place of Presentation
      北海道大学 (札幌市北区)
    • Year and Date
      2015-07-27
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Separation structure of positive radial solutions for semilinear elliptic equations2015

    • Author(s)
      Yuki Naito
    • Organizer
      Equadiff 2015
    • Place of Presentation
      Universite Calude Bernard Lyon 1, Lyon, France
    • Year and Date
      2015-07-07
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Some remarks on separation property of solutions for elliptic equations with exponential nonlinearity2015

    • Author(s)
      Yuki Naito
    • Organizer
      2015 International Workshop on Nonlinear PDE and Application
    • Place of Presentation
      Pusan National University, Busan, Korea
    • Year and Date
      2015-06-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Existence of an asymmetric solution to a nonlinear elliptic equation on the whole sphere2015

    • Author(s)
      Y. Kabeya
    • Organizer
      2015 International Workshop on nonlinear PDE and applications
    • Place of Presentation
      Pusan National University, Busan, Korea
    • Year and Date
      2015-06-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Threshold solutions for semilinear heat equations with polynomial decay initial data2015

    • Author(s)
      内藤雄基
    • Organizer
      ひこね解析セミナー
    • Place of Presentation
      彦根勤労福祉会館(滋賀県彦根市)
    • Year and Date
      2015-06-06
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the criteria for the stability of unduloids2015

    • Author(s)
      高坂良史
    • Organizer
      RIMS研究集会「保存則をもつ偏微分方程式に対する 解の正則性・特異性の研究」
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-06-05
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the solvability of maximizing problems associated with Sobolev type embeddings in \\Bbb R^N2015

    • Author(s)
      Michinori Ishiwata
    • Organizer
      4th Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
    • Place of Presentation
      Grand Hotel San Pietro, Palinuro, Italy
    • Year and Date
      2015-05-29
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the criteria for the stability of the axisymmetric CMC surfaces2015

    • Author(s)
      高坂良史
    • Organizer
      4th Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE’s
    • Place of Presentation
      Grand Hotel San Pietro, Palinuro, Italy
    • Year and Date
      2015-05-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Threshold solutions for semilinear heat equations with polynomial decay initial data2015

    • Author(s)
      内藤雄基
    • Organizer
      東北大学 応用数学セミナー
    • Place of Presentation
      東北大学(仙台市青葉区)
    • Year and Date
      2015-05-21
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] On the existence and nonexistence of maximizers for variational problems associated with Sobolev type embeddings in R^N2015

    • Author(s)
      Michinori Ishiwata
    • Organizer
      AMS special session on “Geometric inequalities and nonlinear partial differential equations
    • Place of Presentation
      University of Nevada, Las Vegas, NV, USA
    • Year and Date
      2015-04-19
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 関数不等式と変分解析:非コンパクト性を巡って2015

    • Author(s)
      石渡 通徳
    • Organizer
      RIMS 共同研究「実解析及び変分解析を用いた関数不等式に付随する偏微分方程式の研究」
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-03-12
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the critical Hardy-Sobolev inequality and related results2015

    • Author(s)
      Michinori Ishiwata
    • Organizer
      第 22 回応用解析研究会シンポジウム
    • Place of Presentation
      静岡県熱海市
    • Year and Date
      2015-03-03
    • Related Report
      2014 Annual Research Report
  • [Presentation] Analysis of stability of the CMC surfaces via the geometric flow with constraints2015

    • Author(s)
      高坂 良史
    • Organizer
      北陸応用数理研究会2015
    • Place of Presentation
      金沢大学サテライト・プラザ(石川県金沢市)
    • Year and Date
      2015-02-21
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of stationary surfaces for the geometric flow with constraints2015

    • Author(s)
      高坂 良史
    • Organizer
      南大阪応用数学セミナー
    • Place of Presentation
      大阪市立大学(大阪市住吉区)
    • Year and Date
      2015-01-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of stationary surfaces for surface diffusion equation2015

    • Author(s)
      高坂 良史
    • Organizer
      第32回九州における偏微分方程式研究集会
    • Place of Presentation
      九州大学西新プラザ(福岡市早良区)
    • Year and Date
      2015-01-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式と平均曲率一定曲面2015

    • Author(s)
      高坂 良史
    • Organizer
      RIMS研究集会「パターン形成と界面ダイナミクスの数理」
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-01-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of solutions for semilinear parabolic equations with critical Sobolev exponent2015

    • Author(s)
      Michinori Ishiwata
    • Organizer
      Closed Seminar on Nonlinear PDE
    • Place of Presentation
      Osaka Universiry, Toyonaka, Osaka
    • Year and Date
      2015-01-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] 球面上での領域のラプラス・ベルトラミ作用素と関連する非線形問題2014

    • Author(s)
      壁谷 喜継
    • Organizer
      大阪大学情報学研究科第11回情報数理学セミナー
    • Place of Presentation
      大阪大学情報学研究科(大阪府吹田市)
    • Year and Date
      2014-11-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of axisymmetric CMC surfaces via surface diffusion equation2014

    • Author(s)
      高坂 良史
    • Organizer
      東北大学応用数学セミナー
    • Place of Presentation
      東北大学(仙台市青葉区)
    • Year and Date
      2014-11-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 球面上での領域のラプラス・ベルトラミ作用素と関連する非線形問題2014

    • Author(s)
      壁谷 喜継
    • Organizer
      数学と現象(Mathematics and Phenomena) in Miyazaki 2014
    • Place of Presentation
      宮崎大学(宮崎県宮崎市)
    • Year and Date
      2014-11-15
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Solutions to the equation of the scalar-field type on a large spherical cap2014

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      RIMS研究集会「偏微分方程式の解の形状と諸性質」
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2014-11-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Analysis of stability of axisymmetric CMC surfaces via surface diffusion equation2014

    • Author(s)
      高坂 良史
    • Organizer
      神戸大学解析セミナー
    • Place of Presentation
      神戸大学(神戸市灘区)
    • Year and Date
      2014-10-28
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Threshold solutions for semilinear heat equations with polynomial decay initial data2014

    • Author(s)
      内藤 雄基
    • Organizer
      九州関数方程式セミナー
    • Place of Presentation
      福岡大学セミナーハウス(福岡市中央区)
    • Year and Date
      2014-10-03
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Critical phenomena in the separation property for seminilear elliptic equaitons2014

    • Author(s)
      内藤 雄基
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学(広島県東広島市)
    • Year and Date
      2014-09-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] Threshold solutions for semilinear heat equations with polynomial decay initial data2014

    • Author(s)
      Yuki Naito
    • Organizer
      6-th Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2014-09-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the effect of equivalent norms on the existence of a maximizer for a variational problem involving the Sobolev type embedding in $\R^N$2014

    • Author(s)
      Michinori Ishiwata
    • Organizer
      Sixth Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2014-09-04
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the existence and nonexistence of a maximizer for a variational problem for the Sobolev type embedding in $\R^N$2014

    • Author(s)
      Michinori Ishiwata
    • Organizer
      The 9th East Asia Partial Differential Equations Conference
    • Place of Presentation
      Hotel Nikko Nara, Nara, Japan
    • Year and Date
      2014-07-28
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the effect of equivalent constraints on a maximizing problem associated with the Sobolev embedding in $\R^N$2014

    • Author(s)
      Michinori Ishiwata
    • Organizer
      The 10th AIMS Conference on Dynamical Systems Differential Equations and Applications
    • Place of Presentation
      Universidad Autonoma de Madrid, Madrid, Spain
    • Year and Date
      2014-07-11
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the critical Hardy-type inequalities and related variational problems2014

    • Author(s)
      Michinori Ishiwata
    • Organizer
      The 10th AIMS Conference on Dynamical Systems Differential Equations and Applications
    • Place of Presentation
      Universidad Autonoma de Madrid, Madrid, Spain
    • Year and Date
      2014-07-10
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Some properties of radial stationary solutions to a parabolic-elliptic system related to Keller-Segel system2014

    • Author(s)
      Takashi Senba
    • Organizer
      10th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Universidad Autonoma de Madrid, Spain
    • Year and Date
      2014-07-09
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 表面拡散方程式に対する定常解の安定性解析2014

    • Author(s)
      高坂 良史
    • Organizer
      信州大学偏微分方程式研究集会
    • Place of Presentation
      信州大学理学部(長野県松本市)
    • Year and Date
      2014-06-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Eigenvalues of the Laplace-Beltrami operator on a spherical cap and related topics2014

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      International Symposium on Applied Analysis
    • Place of Presentation
      University of Zurich, Zurich, Switzerland
    • Year and Date
      2014-06-11
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 非線形熱方程式に対する Cauchy 問題の解の漸近的性質2014

    • Author(s)
      内藤 雄基
    • Organizer
      東京工業大学大岡山談話
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2014-06-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] 球面でのラプラス・ベルトラミ作用素と関連する非線形問題2014

    • Author(s)
      壁谷 喜継
    • Organizer
      九州関数方程式セミナー
    • Place of Presentation
      福岡大学セミナーハウス(福岡市中央区)
    • Year and Date
      2014-05-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Eigenvalues of the Laplace-Beltrami operator on a spherical cap and related nonlinear problems2014

    • Author(s)
      壁谷 喜継
    • Organizer
      名古屋大学微分方程式セミナー
    • Place of Presentation
      名古屋大学多元数理研究科(名古屋市千種区)
    • Year and Date
      2014-05-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 単独反応拡散方程式に見られる複雑な解の挙動

    • Author(s)
      柳田英二
    • Organizer
      東北大学数学専攻談話会
    • Place of Presentation
      東北大学川井ホール(宮城県)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 単独反応拡散方程式における局在解の収束性

    • Author(s)
      柳田英二
    • Organizer
      研究集会「反応拡散系のパターンダイナミクス」
    • Place of Presentation
      富山大学理学部多目的ホール(富山県)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the behavior of solutions to a system of partial differential equations related to biology

    • Author(s)
      Takasi Senba
    • Organizer
      The 22nd International Conference of FIM on Interdisciplinary Mathematics, Statistics and Computational Techniques
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the behavior of radial solutions to a parabolic-elliptic system

    • Author(s)
      Takasi Senba
    • Organizer
      2nd Kyushu-Euskadi Workshop on Applied Mathematics
    • Place of Presentation
      福岡大学セミナーハウス(福岡県福岡市)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Some properties of radial stationary solutions to a parabolic-elliptic system and its application

    • Author(s)
      Takasi Senba
    • Organizer
      Conference on Nonlinear Phenomena in Biology, Physics and Mechanics
    • Place of Presentation
      Helmholtz Zentrum Munchen, Deutschland
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Separation structure of positive radaial solutions for semilinear elliptic equations

    • Author(s)
      Yuki Naito
    • Organizer
      The 2nd Hanbat PDE Conference
    • Place of Presentation
      Hanbat National University, Daejeon, Korea
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Separation structure of positive radial solutions for semilinear elliptic equations

    • Author(s)
      内藤雄基
    • Organizer
      振動理論ワークショップ - 金沢 2014
    • Place of Presentation
      金沢大学サテライト・プラザ(石川県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Global attractivity in the weighted norm fora supercritical semilinear heat equation

    • Author(s)
      Yuki Naito
    • Organizer
      2014 International Workshop on Nonlinear PDE and Applications
    • Place of Presentation
      Pusan National University, Busan, Korea
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Non-azimuthal solutions to a nonlinear elliptic equation on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      2013 Workshop in Nonlinear Equations in Population Biology
    • Place of Presentation
      華東師範大学 (中国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A unified approach to nonlinear elliptic problems on the hyperbolic space or on the sphere

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      Applied Mathematics Seminar
    • Place of Presentation
      University of Zurich, Switzerland
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Bifurcation diagrams of the nonlinear elliptic equation of the scalar-filed type on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      20th Microlocal Analysis and Classical Analysis
    • Place of Presentation
      京都大学理学研究科セミナーハウス(京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Bifurcation diagrams of a nonlinear elliptic equation on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      NTU and NCTS/TPE seminar on PDE
    • Place of Presentation
      国立台湾大学 (台北・台湾)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Bifurcation diagrams of a nonlinear elliptic equation on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      PDE Seminar
    • Place of Presentation
      National Central University, Jhongli City, Taiwan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the global compactness type result for weighted energy functional involving Sobolev critical exponent and its applications

    • Author(s)
      Michinori Ishiwata
    • Organizer
      南大阪応用数学セミナー
    • Place of Presentation
      大阪市立大学理学研究科数学講究室(大阪府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Scale invariant version of the critical Hardy inequality and the associated variational problems

    • Author(s)
      Michinori Ishiwata
    • Organizer
      金沢解析セミナー
    • Place of Presentation
      金沢大学(石川県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On the scale-invariant critical Hardy's inequality and related variational problems

    • Author(s)
      Michinori Ishiwata
    • Organizer
      EQUADIFF 13
    • Place of Presentation
      Charles University, Prague, Czech Republic
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] The scale-invariant log-Hardy inequalities and related variational problems

    • Author(s)
      Michinori Ishiwata
    • Organizer
      3rd Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
    • Place of Presentation
      Tokyo Institute of Technology(東京都)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On an interfacial motion by surface diffusion

    • Author(s)
      高坂良史
    • Organizer
      SIAM Conference on Mathematical Aspects of Materials Science
    • Place of Presentation
      DoubleTree by Hilton Hotel, Philadelphia, USA
    • Related Report
      2013 Annual Research Report
  • [Presentation] Mean curvature flow with a triple junction in multi-dimensional case

    • Author(s)
      高坂良史
    • Organizer
      Workshop on nonlinear PDEs-PDE approach to network and related topics-
    • Place of Presentation
      東北大学川井ホール(宮城県)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Stability analysis of interfaces controlled by surface diffusion

    • Author(s)
      高坂良史
    • Organizer
      Mathematical Aspects of Surface and Interface Dynamics VI
    • Place of Presentation
      東京大学駒場キャンパス(東京都)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式に対する定常曲線・曲面の安定性解析について

    • Author(s)
      高坂良史
    • Organizer
      九大幾何セミナー
    • Place of Presentation
      九州大学伊都キャンパス(福岡県)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On the local existence for mean curvature flow with a triple junction in multi-dimensional case

    • Author(s)
      高坂良史
    • Organizer
      One-day workshop on geometric variational problems
    • Place of Presentation
      北海道大学理学部(北海道)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 表面拡散方程式による平均曲率一定曲面の安定性解析

    • Author(s)
      高坂良史
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学駒場キャンパス(東京都)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] トリプル・ジャンクションをもつ相境界の安定性について

    • Author(s)
      高坂良史
    • Organizer
      数学協働プログラム ワークショップ表面微細構造の学理の探求:低環境負荷材料の創造に向けて
    • Place of Presentation
      北海道大学理学部(北海道)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Asymptotic Behavior of Singular Solutions for a Semilinear Parabolic Equation

    • Author(s)
      Eiji Yanagida
    • Organizer
      9th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, Florida, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Convergence to Barenblatt Profiles for the Fast Diffusion Equation

    • Author(s)
      Eiji Yanagida
    • Organizer
      Second Sino-Chilean Conference on Nonlinear Partial Differential Equations
    • Place of Presentation
      Pontificial Universidad Catolica, Santiago, Chile
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Diffusion-induced phenomena in nonlinear systems

    • Author(s)
      Eiji Yanagida
    • Organizer
      Turing Symposium on Morphogenesis
    • Place of Presentation
      Sendai International Center(宮城県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of singular solutions for a semilinear parabolic equation

    • Author(s)
      Eiji Yanagida
    • Organizer
      IMA Annual Programs: Infinite Dimensional and Stochastic Dynamical Systems and Their Applications, Workshop: Dynamical Systems in Studies of Partial Differential Equations
    • Place of Presentation
      University of Minnesota, Minneapolis, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Non-accessible singular homoclinic orbits for a semilinear parabolic equation

    • Author(s)
      Eiji Yanagida
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      University of Zurich, Switzerland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Singular Solutions of a Seimilinear Parabolic equation

    • Author(s)
      Eiji Yanagida
    • Organizer
      UK-Japan Winter School--Nonlinear Analysis--
    • Place of Presentation
      Royal Academy of Engineering, London, UK
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Oscillating solutions to a simplified chemotaxis system in high dimensional spaces

    • Author(s)
      Takasi Senba
    • Organizer
      5th Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      Centre Insternational de Rencontres Mathematiques, Luminy, Marseille, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Global attractivity properties of stationary solutions for semilinear heat equations

    • Author(s)
      Yuki Naito
    • Organizer
      5th Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      CIRM, Marseille-Luminy, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Global attractivity of self-similar solutions for semilinear heat equations

    • Author(s)
      内藤雄基
    • Organizer
      研究集会「広島微分方程式研究会」
    • Place of Presentation
      広島大学理学部(広島県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 非線形熱方程式の解の漸近挙動と自己相似解

    • Author(s)
      内藤雄基
    • Organizer
      熊本大学数学談話会
    • Place of Presentation
      熊本大学数理演習室(熊本県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Separation structure of positive radial solutions for semilinear elliptic equations

    • Author(s)
      Yuki Naito
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      University of Zurich, Switzerland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 非線形熱方程式の解の漸近挙動と自己相似解

    • Author(s)
      内藤雄基
    • Organizer
      神戸解析セミナー
    • Place of Presentation
      神戸大学理学部(兵庫県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Global behavior of solutions to semilinear heat equations

    • Author(s)
      Yuki Naito
    • Organizer
      International Conference "Quantization blow-up and concentration in mathematical physics view point
    • Place of Presentation
      大阪大学シグマホール(大阪府)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Unified approach to Matukuma type equaitons on the hyperbolic space or on a sphere

    • Author(s)
      Y. Kabeya
    • Organizer
      9th AIMS Conference on Differential Equations
    • Place of Presentation
      Orlando, FL., USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Bifurcation diagrams of nonlinear eplliptic problems on a spherical cap

    • Author(s)
      Y. Kabeya
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      University of Zurich, Zurich, Switzerland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Bifurcation diagrams of a nonlinear eplliptic problem on a spherical cap

    • Author(s)
      Y. Kabeya
    • Organizer
      International Workshop on Stationary Problems in Nonlinear Partial Differential Equations
    • Place of Presentation
      Saga University(佐賀県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Multi-dimensional traveling fronts in bistable reaction-diffusion equations in $\mathbb{R}^{N}$

    • Author(s)
      Masaharu Taniguchi
    • Organizer
      AMS Southeastern Fall Section Meeting
    • Place of Presentation
      Tulane University at New Olreans, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of solutions for semilinear parabolic equation with critical Sobolev exponent

    • Author(s)
      Michinori Ishiwata
    • Organizer
      Regularity and Singularity for Geometric Partial Differential Equations and Conservation Laws
    • Place of Presentation
      Resarch Institute of Mathematical Science, Kyoto University(京都府)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Variational problems associated with Trudinger-Moser inequalities in unbounded domains

    • Author(s)
      Michinori Ishiwata
    • Organizer
      The 9th AIMS conference on Dynamical systems, Differential equations and Applications
    • Place of Presentation
      Hilton Grand Cypress, Orlando, FL, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On the asymptotic behavior of solutions for semiliear parabolic equations involving critical Sobolev exponent

    • Author(s)
      Michinori Ishiwata
    • Organizer
      The 9th AIMS conference on Dynamical systems, Differential equations and Applications
    • Place of Presentation
      Hilton Grand Cypress, Orlando, FL, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of Palais-Smale sequences in the critical problem and its application to semilinear heat equation

    • Author(s)
      Michinori Ishiwata
    • Organizer
      5th Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      Centre International de Rencontres Mathematiques, Luminy, Marseille, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Asymptotic behavior of time-global solutions for semilinear heat equation involving critical Sobolev exponent

    • Author(s)
      Michinori Ishiwata
    • Organizer
      5th Polish-Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences - Modellings, Theory and Simulations -
    • Place of Presentation
      Kansai seminar house(京都府)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Variational problems associated with Trudinger-Moser inequalities in unbounded domains

    • Author(s)
      Michinori Ishiwata
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      University of Zurich, Zurich, Switzerland
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Semilinear parabolic equation with critical Sobolev exponent

    • Author(s)
      Michinori Ishiwata
    • Organizer
      International Conference Quantization Blow-up and Concentration in Mathematical Physics View Point
    • Place of Presentation
      Sigma Hall, Osaka University(大阪府)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] 反応拡散方程式2015

    • Author(s)
      柳田英二
    • Total Pages
      320
    • Publisher
      東京大学出版会
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] International Workshop on Nonlinear PDEs 2016 in Osaka2016

    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] 3rd Chile-Japan Workshop on Nonlinear PDEs2015

    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Year and Date
      2015-12-08
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 6th Euro-Japanese Workshop on Blow-up2014

    • Place of Presentation
      Tokyo Institute of Technology, Tokyo, Japan
    • Year and Date
      2014-09-01
    • Related Report
      2014 Annual Research Report

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Published: 2012-11-27   Modified: 2022-03-01  

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