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Study of solution structures of elliptic equations: supercritical, critical and subcritocal cases

Research Project

Project/Area Number 19H01797
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionThe University of Tokyo

Principal Investigator

Miyamoto Yasuhito  東京大学, 大学院数理科学研究科, 教授 (90374743)

Co-Investigator(Kenkyū-buntansha) 内藤 雄基  広島大学, 先進理工系科学研究科(理), 教授 (10231458)
生駒 典久  慶應義塾大学, 理工学部(矢上), 准教授 (50728342)
石毛 和弘  東京大学, 大学院数理科学研究科, 教授 (90272020)
Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000)
Fiscal Year 2023: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2022: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2021: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2019: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Keywordsソボレフ優臨界 / ジョセフ・ルンドグレン指数 / 球対称特異解 / モース指数 / 分岐図式 / 優臨界楕円型方程式 / 臨界楕円型方程式 / 放物型方程式 / 変分的手法 / 球対称解 / 擬スケール / 非線形楕円型方程式 / 非線形放物型方程式 / 優臨界 / 臨界 / 劣臨界 / 特異解 / 変分問題 / 時間局所可解性 / 変分法 / 劣臨界楕円型方程式
Outline of Research at the Start

楕円型方程式の一つの研究分野として,一つのパラメータλを持つ非線型楕円型偏微分方程式を考え,「λの値の応じて解の個数や性質などがどのように変化するのか?」を考える問題がある.この問題は,純粋数学,物理学,化学,生物学のモデル方程式などの分野に現れる基本的な問題の一つである.関数空間とλの直積空間上に解集合(分岐図式)を描くことが大きな目的である.本研究では非線形項の増大度を,臨界ソボレフ指数と比べることによって,3つの場合(優臨界・臨界・劣臨界)に分けて,分岐図式を解明することを目標とする.

Outline of Final Research Achievements

Solution structures, which are bifurcation diagrams, of supercritical elliptic Dirichlet problem are studied. It is known that standard variational approaches, which are used to study subcritical problems, are not applicable to supercritical problems. A large part of a solution structure was not known. In this study we consider positive solutions of elliptic Dirichlet problem when the domain is a ball. We show that a positive radial singular solution of the supercritical elliptic equation plays a crucial role in the study of bifurcation diagrams. We prove the existence and uniqueness of a positive radial singular solution and obtain an asymptotic expansion of the singular solution near the singular point. We apply our theory to several interesting elliptic equations and classify the bifurcation diagrams.

Academic Significance and Societal Importance of the Research Achievements

ソボレフ優臨界の増大度を持つ楕円型方程式について,2つの古典的な例(Gel'fand問題とジョセフ・ルンドグレンの問題)はよく知られていた.しかし,その他の方程式については,いくつかの限られた方程式についてのみ断片的にしか知られていなかった.
この研究により,(今まで知られている例をすべて含む形で)大幅に一般化された非線形項において,球領域における正値解の分岐構造が明らかになった.特に,多くの非線形項で上記の2つの古典的な場合と定性的に同じ分岐図式となることを明らかにした.
この結果は球領域に限られるが,球領域ではない場合についても,研究の指針を与えるものと期待している.

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Annual Research Report
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • Research Products

    (76 results)

All 2024 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (6 results) Journal Article (31 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 29 results,  Open Access: 6 results) Presentation (39 results) (of which Int'l Joint Research: 10 results,  Invited: 26 results)

  • [Int'l Joint Research] University College Dublin(アイルランド)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Universite Paris-Saclay/Universite de Lorraine/CNRS(フランス)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] University College Dublin(アイルランド)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] University Colledge Dublin(アイルランド)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Suzhou Univ. of Science and Technology(中国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Swansea University(英国)

    • Related Report
      2020 Annual Research Report
  • [Journal Article] Stability and bifurcation diagram for a shadow Gierer?Meinhardt system in one spatial dimension2024

    • Author(s)
      Kaneko Yuki、Miyamoto Yasuhito、Wakasa Tohru
    • Journal Title

      Nonlinearity

      Volume: 37 Issue: 5 Pages: 055011-055011

    • DOI

      10.1088/1361-6544/ad3596

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli2023

    • Author(s)
      Miyamoto Yasuhito
    • Journal Title

      Mathematische Zeitschrift

      Volume: 304 Issue: 4

    • DOI

      10.1007/s00209-023-03328-0

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic formulas of the eigenvalues for the linearization of a one-dimensional sinh-Poisson equation2023

    • Author(s)
      Aizawa Shuya、Miyamoto Yasuhito、Wakasa Tohru
    • Journal Title

      Journal of Elliptic and Parabolic Equations

      Volume: 9 Issue: 2 Pages: 1043-1070

    • DOI

      10.1007/s41808-023-00233-9

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic formulas of the eigenvalues for the linearization of the scalar field equation2023

    • Author(s)
      Miyamoto Yasuhito、Takemura Haruki、Wakasa Tohru
    • Journal Title

      Proceedings of the Royal Society of Edinburgh: Section A Mathematics

      Volume: 1 Issue: 1 Pages: 1-38

    • DOI

      10.1017/prm.2023.95

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Radial single point rupture solutions for a general MEMS model2022

    • Author(s)
      Ghergu Marius、Miyamoto Yasuhito
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 61 Issue: 2 Pages: 1-29

    • DOI

      10.1007/s00526-021-02158-4

    • Related Report
      2022 Annual Research Report 2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Singular solutions for semilinear elliptic equations with general supercritical growth2022

    • Author(s)
      Miyamoto Yasuhito、Naito Yuki
    • Journal Title

      Annali di Matematica Pura ed Applicata (1923 -)

      Volume: 202 Issue: 1 Pages: 341-366

    • DOI

      10.1007/s10231-022-01244-4

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Solvability for time‐fractional semilinear parabolic equations with singular initial data2022

    • Author(s)
      Ghergu Marius、Miyamoto Yasuhito、Suzuki Masamitsu
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Volume: 46 Issue: 6 Pages: 6686-6704

    • DOI

      10.1002/mma.8933

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Convergence to a self-similar solution for a one-phase Stefan problem arising in corrosion theory2022

    • Author(s)
      BOUGUEZZI M.、HILHORST D.、MIYAMOTO Y.、SCHEID J.-F.
    • Journal Title

      European Journal of Applied Mathematics

      Volume: - Issue: 4 Pages: 1-37

    • DOI

      10.1017/s0956792522000250

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Exact Morse index of radial solutions for semlinear elliptic equations with critical exponent on annuli2022

    • Author(s)
      Miyamoto Yasuhito
    • Journal Title

      RIMS Kokyuroku

      Volume: 2244

    • Related Report
      2022 Annual Research Report
  • [Journal Article] 優臨界楕円型方程式の球対称解の構造2022

    • Author(s)
      宮本安人
    • Journal Title

      数理解析研究所講究録

      Volume: 2212 Pages: 54-68

    • Related Report
      2021 Annual Research Report
  • [Journal Article] Radial regular and rupture solutions for a pde problem with gradient term and two parameters2021

    • Author(s)
      Ghergu Marius、Miyamoto Yasuhito
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 150 Issue: 4 Pages: 1697-1709

    • DOI

      10.1090/proc/15861

    • Related Report
      2022 Annual Research Report 2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Stability for stationary solutions of a nonlocal Allen-Cahn equation2021

    • Author(s)
      Y. Miyamoto, T. Mori, T. Tsujikawa and S. Yotsutani
    • Journal Title

      Journal of Differential Equations

      Volume: 275 Pages: 581-597

    • DOI

      10.1016/j.jde.2020.11.024

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Polyharmonic inequalities with nonlocal terms2021

    • Author(s)
      Ghergu Marius、Miyamoto Yasuhito、Moroz Vitaly
    • Journal Title

      Journal of Differential Equations

      Volume: 296 Pages: 799-821

    • DOI

      10.1016/j.jde.2021.06.019

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A doubly critical semilinear heat equation in the L1 space2021

    • Author(s)
      Miyamoto Yasuhito
    • Journal Title

      Journal of Evolution Equations

      Volume: 21 Issue: 1 Pages: 151-166

    • DOI

      10.1007/s00028-020-00573-2

    • Related Report
      2021 Annual Research Report 2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions2021

    • Author(s)
      Naito Yuki
    • Journal Title

      Journal of Differential Equations

      Volume: 297 Pages: 144-174

    • DOI

      10.1016/j.jde.2021.06.024

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semi-classical states for logarithmic Schr?dinger equations2021

    • Author(s)
      Ikoma Norihisa、Tanaka Kazunaga、Wang Zhi-Qiang、Zhang Chengxiang
    • Journal Title

      Nonlinearity

      Volume: 34 Issue: 4 Pages: 1900-1942

    • DOI

      10.1088/1361-6544/abd52a

    • Related Report
      2021 Annual Research Report 2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On weak solutions to a fractional Hardy?H?non equation: Part I: Nonexistence2021

    • Author(s)
      Hasegawa Shoichi、Ikoma Norihisa、Kawakami Tatsuki
    • Journal Title

      Communications on Pure & Applied Analysis

      Volume: 0 Issue: 4 Pages: 1559-1600

    • DOI

      10.3934/cpaa.2021033

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of positive solutions to a certain class of semilinear elliptic equations2021

    • Author(s)
      Ikoma Norihisa
    • Journal Title

      SN Partial Differential Equations and Applications

      Volume: 2 Issue: 2

    • DOI

      10.1007/s42985-021-00079-7

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stable standing waves of nonlinear Schrodinger equations with potentials and general nonlinearities2020

    • Author(s)
      Ikoma N. and Miyamoto Y.
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 59 Issue: 2 Pages: 20-20

    • DOI

      10.1007/s00526-020-1703-0

    • Related Report
      2020 Annual Research Report 2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fundamental properties and asymptotic shapes of the singular and classical radial solutions for supercritical semilinear elliptic equations2020

    • Author(s)
      Miyamoto Yasuhito、Naito Yuki
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 27 Issue: 6 Pages: 1-25

    • DOI

      10.1007/s00030-020-00658-4

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Multiplicity of radial and nonradial solutions to equations with fractional operators2020

    • Author(s)
      Ikoma Norihisa
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 19 Issue: 7 Pages: 3501-3530

    • DOI

      10.3934/cpaa.2020153

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotically self-similar behaviour of global solutions for semilinear heat equations with algebraically decaying initial data2020

    • Author(s)
      Naito Yuki
    • Journal Title

      Proceedings of the Royal Society of Edinburgh: Section A Mathematics

      Volume: 150 Issue: 2 Pages: 789-811

    • DOI

      10.1017/prm.2018.97

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weakly coupled reaction?diffusion systems with rapidly growing nonlinearities and singular initial data2019

    • Author(s)
      Miyamoto Yasuhito、Suzuki Masamitsu
    • Journal Title

      Nonlinear Analysis

      Volume: 189 Pages: 111576-111576

    • DOI

      10.1016/j.na.2019.111576

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicity of bounded solutions to the $k$-Hessian equation with a Matukuma-type source2019

    • Author(s)
      Miyamoto Yasuhito、Sanchez Justino、Vergara Vicente
    • Journal Title

      Revista Matem?tica Iberoamericana

      Volume: 35 Issue: 5 Pages: 1559-1582

    • DOI

      10.4171/rmi/1092

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Exact eigenvalues and eigenfunctions for a one-dimensional Gel’fand problem2019

    • Author(s)
      Miyamoto Yasuhito、Wakasa Tohru
    • Journal Title

      Journal of Mathematical Physics

      Volume: 60 Issue: 2 Pages: 021506-021506

    • DOI

      10.1063/1.5021825

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] THE EMDEN-FOWLER EQUATION ON A SPHERICAL CAP OF S^N2019

    • Author(s)
      Kosaka Atsushi、Miyamoto Yasuhito
    • Journal Title

      Nonlinear Analysis

      Volume: 14 Issue: 14 Pages: 1-25

    • DOI

      10.1016/j.na.2018.07.010

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016820

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state2019

    • Author(s)
      Naito Yuki、Senba Takasi
    • Journal Title

      Nonlinear Analysis

      Volume: 181 Pages: 265-293

    • DOI

      10.1016/j.na.2018.12.001

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solvability of the heat equation with a nonlinear boundary condition2019

    • Author(s)
      Hisa, Kotaro; Ishige, Kazuhiro
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 51 Issue: 1 Pages: 565-594

    • DOI

      10.1137/17m1131416

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A supercritical scalar field equation with a forcing term2019

    • Author(s)
      K. Ishige, S. Okabe and T. Sato
    • Journal Title

      J. Math. Pures Appl.

      Volume: 128 Pages: 183-212

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rate of convergence in the large diffusion limit for the heat equation with a dynamical boundary condition2019

    • Author(s)
      M. Fila, K. Ishige, T. Kawakami and J. Lankeit
    • Journal Title

      Asymptot. Anal.

      Volume: 114 Pages: 37-57

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Foliation by Area-constrained Willmore Spheres Near a Nondegenerate Critical Point of the Scalar Curvature2018

    • Author(s)
      Norihisa Ikoma, Andrea Malchiodi and Andrea Mondino
    • Journal Title

      International Mathematics Research Notices

      Volume: 印刷中 Issue: 19 Pages: 6539-6568

    • DOI

      10.1093/imrn/rny203

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli2024

    • Author(s)
      Yasuhito Miyamoto
    • Organizer
      Japan-Korea Workshop on Nonlinear PDEs and Its Applications
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli2024

    • Author(s)
      宮本安人
    • Organizer
      日本数学会2024年度年会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli2023

    • Author(s)
      Yasuhito Miyamoto
    • Organizer
      The 13th AIMS Conference (University of North Carolina Wilmington, USA)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Structure of radial solutions for supercritical elliptic equations2023

    • Author(s)
      Yasuhito Miyamoto
    • Organizer
      日韓共同研究集会(MSJ-KMS Joint Meeting 2023)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 優臨界楕円型方程式の球対称解の構造2023

    • Author(s)
      宮本安人
    • Organizer
      2023年度日本数学会秋季総合分科会(実函数論分科会)
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] 1次元shadow Gierer-Meinhardt系の完全分岐図式とHopf分岐2023

    • Author(s)
      宮本安人
    • Organizer
      第3回はこだて現象数理研究集会
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] 固有値の明示的表示と Lame 方程式2023

    • Author(s)
      宮本安人
    • Organizer
      現象と数理 北九州小研究集会
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] 最近の研究2022

    • Author(s)
      宮本安人
    • Organizer
      基盤研究(S)(研究代表者:石毛和弘氏)の中間報告会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Singular solution for semilinear elliptic equations with general supercritical growth2022

    • Author(s)
      宮本安人,内藤雄基
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli2022

    • Author(s)
      宮本安人
    • Organizer
      第81回東工大数理解析セミナー
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Exact Morse index of radial solutions for semilinear elliptic equations with critical exponent on annuli2022

    • Author(s)
      宮本安人
    • Organizer
      RIMS共同研究(公開型)『常微分方程式の定性的理論とその現象解析への応用』
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Structure of positive radial solutions for semilinear elliptic problem with general supercritical growth2022

    • Author(s)
      Yasuhito Miyamoto
    • Organizer
      UFPB's Webinar on Partial Differential Equations and Geometric Analysis
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Solvability for time-fractional smiilinear parabolic equations with singular initial data2022

    • Author(s)
      Yasuhito Miyamoto, Marius Ghergu, Masamitsu Suzuki
    • Organizer
      第48回 発展方程式研究会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Polyharmonic inequalities with nonlocal terms2022

    • Author(s)
      Marius Ghergu 宮本 安人 Vitaly Moroz
    • Organizer
      日本数学会2022年度年会 函数方程式論分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Stable standing waves of nonlinear Schrodinger equations with potentials and general nonlinearities2021

    • Author(s)
      生駒 典久, 宮本 安人
    • Organizer
      日本数学会2021年度秋季総合分科会 函数方程式論分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Bifurcation structure of radial solutions for supercritical elliptic equation part 1, 2,2021

    • Author(s)
      宮本安人
    • Organizer
      RIMS 共同研究(公開型) 『偏微分方程式の解の幾何的様相』
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Singular solution and separation property for semilinear elliptic equations with general supercritical growth2021

    • Author(s)
      Yasuhito Miyamoto
    • Organizer
      International Workshop on Nonlinear Elliptic Equations and Its Applications
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Fundamental properties of the singular radial solutions for supercritical semilinear elliptic equations2021

    • Author(s)
      Y. Naito
    • Organizer
      Differential Equations Day on Zoom, University of Ulsan
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow-up criteria for the parabolic-elliptic Keller-Segel system in higher dimensions2021

    • Author(s)
      内藤雄基
    • Organizer
      第2回「オンライン放物型偏微分方程式ワークショップ」
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Blow-up criteria for the parabolic-elliptic Keller-Segel system in higher dimensions2021

    • Author(s)
      内藤雄基
    • Organizer
      日本数学会2021年度秋季総合分科会 函数方程式論分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] A doubly critical semilinear heat equation in the L1 space2021

    • Author(s)
      宮本安人
    • Organizer
      第38回九州における偏微分方程式研究集会
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] A doubly critical semilinear heat equation in the L1 space2021

    • Author(s)
      宮本安人
    • Organizer
      第4回 反応拡散方程式と非線形分散型方程式の解の挙動
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Existence and uniqueness of singular solutions for supercritical semilinear elliptic equations2021

    • Author(s)
      宮本安人,内藤雄基
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions2021

    • Author(s)
      内藤雄基
    • Organizer
      九州関数方程式セミナー
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Radial single point rupture solutions for a general MEMS model2020

    • Author(s)
      Yasuhito Miyamoto, Marius Ghergu
    • Organizer
      日本数学会2020年度秋季総合分科会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 劣線形項を持つ非線形楕円型方程式の非負値解の挙動2020

    • Author(s)
      生駒典久
    • Organizer
      九州関数方程式セミナー
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Pattern formations and the “hot spots” conjecture2020

    • Author(s)
      Yasuhito Miyamoto
    • Organizer
      UCD SMS Seminar
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Parametric representation of a sheet constructed by all solution to a nonlocal Allen-Cahn equation2020

    • Author(s)
      森 竜樹,久藤 衡介,宮本 安人,辻川 亨,四ツ谷 晶二
    • Organizer
      日本数学会2020年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Stable standing waves of nonlinear schrodinger equations with potentials and general nonlinearities2019

    • Author(s)
      宮本安人
    • Organizer
      愛媛大学における微分方程式セミナー(通算第42回)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Stable standing waves of nonlinear schrodinger equations with potentials and general nonlinearities2019

    • Author(s)
      宮本安人
    • Organizer
      第51回「南大阪応用数学セミナー」,大阪市立大学
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Existence, uniqueness and convergence of the singular radial solution for supercritical semilinear elliptic equations2019

    • Author(s)
      宮本安人
    • Organizer
      発展方程式における系統的形状解析及び漸近解析
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] 分数冪拡散方程式の時間局所可解性について2019

    • Author(s)
      宮本安人,Theo Giraudon
    • Organizer
      第45回発展方程式研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Incomplete blow-up of solutions for semilinear heat equations with supercritical nonlinearity2019

    • Author(s)
      内藤 雄基
    • Organizer
      信州大学偏微分方程式研究集会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Threshold solutions for semilinear heat equations with polynomial decay initial data2019

    • Author(s)
      Yuki Naito
    • Organizer
      Equadiff 2019, Leiden, オランダ
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 特異定常解より大きい爆発形状を持つ不完全爆発解の 存在について2019

    • Author(s)
      内藤 雄基、仙葉 隆
    • Organizer
      日本数学会2019年度秋季総合分科会, 金沢大学
    • Related Report
      2019 Annual Research Report
  • [Presentation] Threshold solutions for semilinear heat equations with slowly decaying initial data2019

    • Author(s)
      Yuki Naito
    • Organizer
      2019 International Workshop on Nonlinear PDEs and Its Application, Jeju National University, Jeju, Korea
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow-up criteria for the simplest Keller-Segel model of chemotaxis in higher dimensions2019

    • Author(s)
      Yuki Naito
    • Organizer
      Chemotaxis and Nonlinear Parabolic Equations, -In honor of Professor Takasi Senba on his 60th birthday-, Kitakyushu International Conference Center
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow-up criteria for the parabolic-elliptic Keller-Segel system in higher dimensions2019

    • Author(s)
      内藤 雄基
    • Organizer
      数学と現象:Mathematics and Phenomena in Miyazaki 2019
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Existence of solutions for a higher-order semi linear parabolic equation with singular initial data2019

    • Author(s)
      石毛和弘
    • Organizer
      Chemotaxis and Nonlinear Parabolic Equations,北九州国際会議場(小倉)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited

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Published: 2019-04-18   Modified: 2025-01-30  

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