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Study on oscillation and singularity in mass resonance

Research Project

Project/Area Number 25610027
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionWaseda University

Principal Investigator

Tohru Ozawa  早稲田大学, 理工学術院, 教授 (70204196)

Co-Investigator(Kenkyū-buntansha) TANAKA Kazunaga  早稲田大学, 理工学術院, 教授 (20188288)
Co-Investigator(Renkei-kenkyūsha) KATAYAMA Soichiro  和歌山大学, 教育学部, 教授 (70283942)
SUNAGAWA Hideaki  大阪大学, 理学(系)研究科(研究院), 准教授 (80375394)
MACHIHARA Shuji  埼玉大学, 教育学部, 准教授 (20346373)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords関数方程式の大域理論 / 数学解析 / 関数方程式 / 関数空間論 / 実解析 / 函数方程式 / 函数空間論 / 変分解析
Outline of Final Research Achievements

Mass resonance phenomenon of systems of nonlinear Schr\"odinger equations is studied. We have found an appropriate Lagrangean for the system of Schr\"odinger equations with quadratic interactions, by which we are able to give a clear explanation of the roles of mass resonance phenomenon as well as of complex conjugate in wavefunctions.
A variational setting has been introduced for the analysis on standing waves associated with mass resonance. We proved the existence and (essential) uniqueness of ground states.
Moreover, examples of interactions were found for the blow-up solutions with arbitrarily small Cauchy data under mass resonance condition.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (79 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (3 results) Journal Article (28 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 28 results,  Open Access: 7 results,  Acknowledgement Compliant: 1 results) Presentation (38 results) (of which Int'l Joint Research: 11 results,  Invited: 37 results) Book (1 results) Remarks (1 results) Funded Workshop (8 results)

  • [Int'l Joint Research] モンペリエ大学(CNRS)(フランス)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] バーミンガム大学(英国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] 南京林学大学(中国)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Weighted Lp-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces2016

    • Author(s)
      K. Fujiwara, T. Ozawa
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68 Pages: 169-191

    • NAID

      130005122687

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity criteria for harmonic heat flow and related system2016

    • Author(s)
      J. Fan, T. Ozawa
    • Journal Title

      Mathematische Nachrichten

      Volume: 289 Issue: 1 Pages: 28-33

    • DOI

      10.1002/mana.201200219

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions2016

    • Author(s)
      G. Hoshino, T. Ozawa
    • Journal Title

      Electronic Journal of Differential Equations

      Volume: 2016 Pages: 1-8

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations2016

    • Author(s)
      G. Hoshino, T. Ozawa
    • Journal Title

      Nonlinear Differ. Equ. Appl., NoDEA

      Volume: 23 Issue: 1 Pages: 1-10

    • DOI

      10.1007/s00030-016-0362-5

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Some sharp bilinear space-time estimates for the wave equation2016

    • Author(s)
      N. Bez, C. Jeavons, T. Ozawa
    • Journal Title

      Mathematika

      Volume: 62 Issue: 3 Pages: 719-737

    • DOI

      10.1112/s0025579316000012

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Finite Time blowup fot the fourth-order NLS2016

    • Author(s)
      Y. Cho, T. Ozawa, C. Wang
    • Journal Title

      Bulletin of the Korean Mathematical Society

      Volume: 53 Issue: 2 Pages: 615-640

    • DOI

      10.4134/bkms.2016.53.2.615

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Finite time extinction for nonlinear Schrödinger equation in 1D and 2D2015

    • Author(s)
      R. Carles, T. Ozawa
    • Journal Title

      Commun. PDE.

      Volume: 40 Issue: 5 Pages: 897-917

    • DOI

      10.1080/03605302.2014.967356

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Well-posedness for the Cauchy problem for a system of semirelativistic equations2015

    • Author(s)
      K. Fujiwara, S. Machihara, T. Ozawa
    • Journal Title

      Commun. Math. Phys.

      Volume: 338 Issue: 1 Pages: 367-391

    • DOI

      10.1007/s00220-015-2347-3

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On a system of semirelativistic equations in the energy space2015

    • Author(s)
      K. Fujiwara, S. Machihara, T. Ozawa
    • Journal Title

      Commun. Pure Appl. Anal.

      Volume: 14 Pages: 1343-1355

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Regularity criteria for the incompressible MHD with the Hall or ion-slip effects2015

    • Author(s)
      J. Fan, T. Ozawa
    • Journal Title

      International Journal of Mathematical Analysis

      Volume: 9 Pages: 1173-1186

    • DOI

      10.12988/ijma.2015.5253

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Analytic smoothing effect for a system of Schrodinger equations with two wave interaction2015

    • Author(s)
      G. Hoshino, T. Ozawa
    • Journal Title

      Adv. Differential Equations

      Volume: 20 Pages: 697-716

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak solutions to the Ginzburg-Landau model in superconductivity with the temporal gauge2015

    • Author(s)
      J. Fan, T. Ozawa
    • Journal Title

      Applicable Analysis

      Volume: - Issue: 9 Pages: 2029-2038

    • DOI

      10.1080/00036811.2015.1084415

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Analytic smoothing effect for a system of Schrödinger equations with three wave interaction2015

    • Author(s)
      G. Hoshino, T. Ozawa
    • Journal Title

      Journal of Mathematical Physics

      Volume: 56 Issue: 9 Pages: 091513-091513

    • DOI

      10.1063/1.4931659

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on global solutions to the Cauchy problem for semirelativistic equations with power type nonlinearity2015

    • Author(s)
      K. Fujiwara, T. Ozawa
    • Journal Title

      International Journal of Mathematical Analysis

      Volume: 9 Pages: 2599-2610

    • DOI

      10.12988/ijma.2015.58211

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space2015

    • Author(s)
      S. Machihara, T. Ozawa, H. Wadade
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 2015:281 Issue: 1 Pages: 281-281

    • DOI

      10.1186/s13660-015-0806-1

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [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
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Multiplicity of positive solutions of nonlinear Schroedinger equations concentrating at a potential well.2015

    • Author(s)
      S. Cingolani, L. Jeanjean, K. Tanaka
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: 53 Issue: 1-2 Pages: 413-439

    • DOI

      10.1007/s00526-014-0754-5

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Continuum of solutions for an elliptic problem with critical growth in the gradient2015

    • Author(s)
      D. Arcoya, C. De Coster, L. Jeanjean, K. Tanaka
    • Journal Title

      J. Funct. Anal.

      Volume: 268 Issue: 8 Pages: 2298-2335

    • DOI

      10.1016/j.jfa.2015.01.014

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Analytic smoothing effect for nonlinear Schr\"odinger equation withquintic nonlinearity2014

    • Author(s)
      G. Hoshino, T. Ozawa
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 419 Issue: 1 Pages: 285-297

    • DOI

      10.1016/j.jmaa.2014.04.057

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions2014

    • Author(s)
      D. Arcoya, C. De Coster, L. Jeanjean, K. Tanaka
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 420 Issue: 1 Pages: 772-780

    • DOI

      10.1016/j.jmaa.2014.06.007

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion2014

    • Author(s)
      J. Fan, T. Ozawa
    • Journal Title

      Kinetic and Related Models

      Volume: 7 Issue: 1 Pages: 45-56

    • DOI

      10.3934/krm.2014.7.45

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Small data blow-up for a system of nonlinear Schrodinger equations2013

    • Author(s)
      T. Ozawa, H. Sunagawa
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 399 Pages: 147-155

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finite charge solutions to cubic Schrodinger equations with a nonlocal nonlinearity in one space dimension2013

    • Author(s)
      K. Nakamura, T. Ozawa
    • Journal Title

      Discrete and Continuous Dynamical Systems A

      Volume: 33 Pages: 789-801

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On a system of nonlinear Schrodinger equations with quadratic interaction2013

    • Author(s)
      N. Hayashi, T. Ozawa, K. Tanaka
    • Journal Title

      Ann. Inst. Henri Poincare, Analyse non lineaire

      Volume: 30 Pages: 661-690

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sharp Morawetz estimates2013

    • Author(s)
      K. Rogers, T. Ozawa
    • Journal Title

      J. d' Anal. Math

      Volume: 121 Issue: 1 Pages: 163-175

    • DOI

      10.1007/s11854-013-0031-0

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Multi-bump positive solutions for a nonlinear elliptic problem in expanding tubular domains2013

    • Author(s)
      J. Byeon, K. Tanaka
    • Journal Title

      Calc. Var. PDE

      Volume: 50 Issue: 1-2 Pages: 1-1

    • DOI

      10.1007/s00526-013-0639-z

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Semi-classical standing waves for nonlinear Schrodinger equations at structurally stable critical points of the potential2013

    • Author(s)
      J. Byeon, K. Tanaka
    • Journal Title

      J. Eur. Math. Soc

      Volume: 15 Issue: 5 Pages: 1859-1899

    • DOI

      10.4171/jems/407

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Semiclassical standing waves with clustering peaks for nonlinear Schrodinger equations2013

    • Author(s)
      J. Byeon, K. Tanaka
    • Journal Title

      Memoirs of the American Mathematical Society

      Volume: 229

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Life span of solutions to nonlinear Schr\"odinger equations on torus2016

    • Author(s)
      Tohru Ozawa
    • Organizer
      Workshop on Partial Differential Equations
    • Place of Presentation
      Zhejiang Normal University
    • Year and Date
      2016-03-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Singular perturbation problems for nonlinear elliptic equations- variational methods for degenerate setting -2016

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      第8回名古屋微分方程式研究集会, The 8th Nagoya Workshop on Differential Equations
    • Place of Presentation
      名古屋大学理学部
    • Year and Date
      2016-03-23
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 非線形楕円型方程式に対する特異摂動問題 - 特に退化する場合を巡って -2016

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      日本数学会年会, 特別講演
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-17
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Existence of concentrating solutions for nonlinear ellipticequations in singularly perturbed domains2016

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      Seminari di matematica, Politecnico di Bari
    • Place of Presentation
      Politecnico di Bari, Italy
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A new deformation method for singular perturbation problems and applications2015

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      3rd Chile-Japan Workshop on Nonlinear PDEs
    • Place of Presentation
      大阪大学豊中キャンパスシグマホール
    • Year and Date
      2015-12-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A new deformation argument for singular perturbation problems and applications2015

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      第32回金沢解析セミナー
    • Place of Presentation
      金沢大学理学部
    • Year and Date
      2015-11-06
    • Related Report
      2015 Annual Research Report
  • [Presentation] On the Hardy type inequalities2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      Second Workshop on Nonlinear Dispersive Equations
    • Place of Presentation
      IMECC-UNICAMP, Campinas, Brazil
    • Year and Date
      2015-10-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the Hardy type inequalities2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      The 3rd CAU-Kyoto U. Joint Workshop on Nonlinear PDEs
    • Place of Presentation
      Seo-gwi-po KAL hotel, Jejudo, Korea
    • Year and Date
      2015-09-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Singular perturbation problems for nonlinear elliptic problems2015

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      Workshop in Nonlinear PDEs
    • Place of Presentation
      Universiteacute; Libre de Bruxelles
    • Year and Date
      2015-09-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On critical Hardy inequality2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      analysis seminar in Peking University
    • Place of Presentation
      Peking University
    • Year and Date
      2015-09-02
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] $L^p$ 型のハーディーの不等式について2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      金沢解析研究会2015
    • Place of Presentation
      金沢大学サテライト・プラザ  3階集会室
    • Year and Date
      2015-08-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A new deformation method for singular perturbation problems2015

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      東北大学理学部数学科談話会
    • Place of Presentation
      東北大学理学部数学科
    • Year and Date
      2015-08-05
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Quadratic interactions in systems of dispersive equations2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      10th International ISAAC Congress
    • Place of Presentation
      University of Macau
    • Year and Date
      2015-08-03
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hardy type inequalities2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      workshop on partial differential equations and numerical analysis (Nonlinear PDE Meeting at Yanbian University july 2015, Yanji)
    • Place of Presentation
      Yanbian University
    • Year and Date
      2015-07-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hardy型の不等式について ( On the Hardy type inequalities )2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      Monday Analysis Seminar(No. 5)
    • Place of Presentation
      北海道大学理学部3号館210室
    • Year and Date
      2015-06-22
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Hardy型の不等式について ( On the Hardy type inequalities )2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      信州大学偏微分方程式研究集会
    • Place of Presentation
      信州大学理学部数学科(旧・数理自然情報科学科)
    • Year and Date
      2015-06-12
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Finite Time Extinction for Nonlinear Schrodinger Equation2015

    • Author(s)
      Tohru Ozawa
    • Organizer
      Workshop on Nonlinear Partial Differential Equations
    • Place of Presentation
      Zhejiang University, Hangzhou, China
    • Year and Date
      2015-03-14
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Quadratic Interactions in Dispersive Systems2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      「微分方程式の総合的研究」
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2014-12-20
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Nonlinear elliptic problems in singularly perturbed cylindrical domains2014

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      Workshop on Nonlinear PDE at Tohoku University
    • Place of Presentation
      東北大学工学部青葉山記念館
    • Year and Date
      2014-11-13 – 2014-11-15
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Improvement of Holder's inequality2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      Modern Harmonic Analysis and Applications
    • Place of Presentation
      Venue/School of Science Building 1,3F, Room No.1337 Saitama University
    • Year and Date
      2014-10-30
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Singular perturbation problems for nonlinear elliptic equations in expanding tubular type domains and NLS systems2014

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      "NCTS Workshop on Calculus of Variations and Related Topics"
    • Place of Presentation
      National Center for Theoretical Sciences Mathematics Devision, National Tsing-Hua University,Taiwan
    • Year and Date
      2014-10-28 – 2014-11-01
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Finite Time Extinction for Nonlinear Schrödinger Equation2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      10th “Topics in Nonlinear Problems”
    • Place of Presentation
      Oita Prefecture Chushokigyo Kaikan
    • Year and Date
      2014-09-17
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 古典場の理論に現れる非線型波動方程式2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      中央大学理工学部数学教室 Encounter with Mathematics 62波動方程式-古典物理から相対論まで-
    • Place of Presentation
      中央大学理工学部数学教室
    • Year and Date
      2014-09-15
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Systems of Quadratic Dispersive Equations2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      Roman Summer School and Workshop KAM Theory and Dispersive PDEs.
    • Place of Presentation
      Roma, Italy
    • Year and Date
      2014-09-08
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Singularly perturbed nonlinear elliptic problems in expanding tubular type domains2014

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      The 10th AIMS Conference on Dynamical Systems,Differential Equations and Applications
    • Place of Presentation
      Universidad Autónoma de Madrid, Madrid, Spain
    • Year and Date
      2014-07-05 – 2014-07-13
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Nonlinear Schrödinger Equation in Two Dimensional Domains2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      2014 International Conference of the Honam Mathematical Society Chosun University
    • Place of Presentation
      Honam Mathematical Society Chosun University, Gwangju, Republic o Korea
    • Year and Date
      2014-06-27
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the Brezis-Gallouet technique2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      偏微分方程式セミナー
    • Place of Presentation
      北海道大学理学部3号館3-309室
    • Year and Date
      2014-06-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] チューブ状領域における非線形楕円型方程式の解の存在問題2014

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      第5回「ハミルトン系とその周辺」研究集会
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Year and Date
      2014-05-29 – 2014-05-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the Brezis-Gallouet technique2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      名古屋微分方程式セミナー
    • Place of Presentation
      名古屋大学多元数理科学棟 453セミナー
    • Year and Date
      2014-05-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] R^N およびシリンダー状領域における非線形楕円型方程式の正値解の存在2014

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      第17回南大阪応用数学セミナー
    • Place of Presentation
      大阪府立大学中百舌鳥キャンパス
    • Year and Date
      2014-04-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 二次元領域における非線型シュレディンガー方程式の初期値問題2014

    • Author(s)
      Tohru Ozawa
    • Organizer
      Seminar on Nonlinear Analysis at O-okayama 非線形解析セミナー
    • Place of Presentation
      東京工業大学大岡山キャンパス 西8号館W棟11階 W1101号室
    • Year and Date
      2014-04-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] チューブ状領域における非線形楕円型方程式の正値解の多重性2014

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      松山解析セミナー
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Mass resonance in a system of nonlinear Schrodinger equations2013

    • Author(s)
      Tohru Ozawa
    • Organizer
      The Asian Mathematical Conference 2013 (AMC 2013)
    • Place of Presentation
      BEXCO, Busan, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Multi-peak solutions for singularly perturbed elliptic problems2013

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      the workshop on nonlinear PDE
    • Place of Presentation
      Chern Inst. Math., Nankai University, Tianjin, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On a system of Schrodinger equations

    • Author(s)
      Tohru Ozawa
    • Organizer
      Harmonic Analysis and PDEs on Manifolds
    • Place of Presentation
      中央大学後楽園キャンパス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Mass resonance in a system of nonlinear Schrodinger equations

    • Author(s)
      Tohru Ozawa
    • Organizer
      Linear and Nonlinear PDE
    • Place of Presentation
      Univ. of Pisa, Italy
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Bilinear estimates in the Sobolev spaces

    • Author(s)
      Tohru Ozawa
    • Organizer
      Analyse Numerique et Equations aux Derivees Partielles
    • Place of Presentation
      Universite Paris-Sud Laboratoire de Mathématiques
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Multiple positive solutions for nonlinear elliptic equations in expanding annular type domains

    • Author(s)
      Kazunaga Tanaka
    • Organizer
      首都大学幾何セミナー
    • Place of Presentation
      首都大学東京
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] Harmonic Analysis and Nonlinear Partial Differential Equations2013

    • Author(s)
      M. Sugimoto and T. Ozawa(Eds.)
    • Total Pages
      170
    • Publisher
      RIMS Kokyuroku Bessatsu
    • Related Report
      2013 Research-status Report
  • [Remarks] 小澤徹研究室

    • URL

      http://www.ozawa.phys.waseda.ac.jp/index2.html

    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Workshop on Partial Differential Equation2016

    • Place of Presentation
      浙江師範大学(中華人民共和国浙江省)
    • Year and Date
      2016-03-24
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Harmonic Analysis, Geometric Analysis and PDE Workshop2016

    • Place of Presentation
      埼玉大学(さいたま市桜区)
    • Year and Date
      2016-03-03
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 第33回九州における偏微分方程式研究集会2016

    • Place of Presentation
      九州大学西新プラザ(福岡市早良区)
    • Year and Date
      2016-01-27
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 若手による流体力学の基礎方程式研究集会2016

    • Place of Presentation
      名古屋大学(名古屋市千種区)
    • Year and Date
      2016-01-06
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 共共拠点研究会RIMS1963-IMI20132015

    • Place of Presentation
      九州大学伊都キャンパス(福岡市西区)
    • Year and Date
      2015-12-07
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 日本数学会2015年秋季総合分科会2015

    • Place of Presentation
      京都産業大学(京都市北区)
    • Year and Date
      2015-09-13
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 信州大学偏微分方程式研究集会2015

    • Place of Presentation
      信州大学(松本市旭)
    • Year and Date
      2015-06-12
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] 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」2015

    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2015-06-03
    • Related Report
      2015 Annual Research Report

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Published: 2014-07-25   Modified: 2022-01-31  

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