Reserch of the asymptotic bahevior of infinite-time blow up solutions for parabolic equations associated with ciritcal Sobole-Hardy exponent

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19740081
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Muroran Institute of Technology
• Principal Investigator: ISHIWATA Michinori Muroran Institute of Technology, 大学院・工学研究科, 准教授 (30350458)
• Project Period (FY): 2007 – 2010
• Keywords: 関数方程式の大域理論

Research Abstract

本研究では臨界ソボレフ-ハーディ指数をもつ放物型方程式の時間大域解、とくに無限時間爆発解の漸近挙動を明らかにすることを目的とする。そのため、
(1) 臨界型放物型方程式の解の可解性に関する抽象理論の展開
(2) 時間発展しない定常問題でのコンパクト性の破れの解析
(3) ソボレフ-ハーディ型不等式のもつ数理的構造
の三つのトピックについて、周辺的な研究も含め明らかにする必要がある。

Research Products

• [Journal Article] The decay of the solutions for the heat equation with a potential (2009)
  • Author(s): Kazuhiro Ishige, Michinori Ishiwata, Tatsuki Kawakami
  • Journal Title: Indiana University Mathematics Journal 58,No.6 Pages: 2673-2708
• [Journal Article] Effect of topology on the multiplicity of solutions for some semilinear elliptic systems with critical Sobolev exponent (2009)
  • Author(s): Ishiwata Michinori
  • Journal Title: Nonlinear Differ. Equ. Appl. 16 Pages: 283-296
• [Journal Article] Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in R2 (2009)
  • Author(s): Michinori Ishiwata, Takayoshi Ogawa, Futoshi Takahashi
  • Journal Title: Electron. J. Diff. Eqns. Vol.2009,No.32 Pages: 1-10
• [Journal Article] Asymptotic behavior of strong solutions for nonlinear parabolic equations with critical Sobolev exponent (2008)
  • Author(s): Michinori Ishiwata
  • Journal Title: Advances in Differential Equations 13(3-4) Pages: 349-366
  • Peer Reviewed
• [Journal Article] Multiple solutions for semilinear elliptic systems involving critical Sobolev exponent (2007)
  • Author(s): Michinori Ishiwata
  • Journal Title: Differential and Integral Equations 20(11) Pages: 1237-1252
  • Peer Reviewed
• [Presentation] Exsitence of maximizing functions for functionals of critical growth (2009)
  • Author(s): Michinori Ishiwata
  • Organizer: 1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
  • Place of Presentation: Tohoku University, Sendai, Japan
  • Year and Date: 20090715-20090719
• [Presentation] The asymptotic behavior of solutions of semilinear parabolic equation with critical Sobolev exponent
  • Author(s): Michinori Ishiwata
  • Organizer: 4th Polish - Japanese Days Current advances in applied nonlinear analysis and mathematical modelling issues
  • Place of Presentation: Warsaw/Madralin, Poland
• [Presentation] On the threshold solutions for semilinear parabolic problems involving critical Sobolev exponent
  • Author(s): Michinori Ishiwata
  • Organizer: Third Euro-Japanese workshop on blow-up, 2008
  • Place of Presentation: Tohoku University, Sendai
• [Presentation] On the concentration phenomena of solutions for semilinear parabolic equations involving critical Sobolev exponent
  • Author(s): Michinori Ishiwata
  • Organizer: Ryukoku Workshop 2008, Recent Progress on Pattern Formation and Dynamics in Mathematical Sciences
  • Place of Presentation: Ryukoku university, Kyoto
• [Presentation] Asymptotic behavior of time-global solutions for a semilinear parabolic equation involving critical Sobolev exponent
  • Author(s): Michinori Ishiwata
  • Organizer: First Chile-Japan workshop on Nonlinear Elliptic and Parabolic PDE, Centro de modelamiento mathematico
  • Place of Presentation: departmento de ingenieria matematica, universidad de Chile, Santiago, Chile
• [Book] これからの非線型偏微分方程式 (2007)
  • Author(s): 石渡通徳
  • Total Pages: 203-221
  • Publisher: 日本評論社