Theory of global well-posedness on the nonlinear partial differential equations-

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20224013
• Research Category: Grant-in-Aid for Scientific Research (S)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Waseda University (2011-2012); Tohoku University (2009-2010)
• Principal Investigator: KOZONO Hideo Tohoku University, 大学院・理学研究科, 教授 (00195728)
• Project Period (FY): 2008 – 2012
• Keywords: 関数方程式 / 非線形偏微分方程式

Research Abstract

非線形偏微分方程式を広範囲に渡って対象とし、解の存在、一意性、安定性といった"適切性"を研究する。定常方程式については、単に全空間だけでなく、種数のなど領域の位相不変量が方程式の可解性に与える影響をも対象とする。また障害物の形状に依存した解の非等方的な振る舞い、あるいは無限遠方における解の挙動の一意性への寄与を考察する。時間発展方程式については、局所適切性にとどまらず、時間大域的可解性を明らかにする。

Research Products

• [Journal Article] Blow-up set for a semilinear heat equation with small diffusion (2010)
  • Author(s): Y.Fujishima, K.Ishige
  • Journal Title: J.Differential Equations 249 Pages: 1056-1077
  • Peer Reviewed
• [Journal Article] Parabolic quasi-concavity for solutions to parabolic problems in convex rings (2010)
  • Author(s): K.Ishige, P.Salani
  • Journal Title: Math.Nachr.(雑誌Math.Nachr.のEditor Choice を受賞) 283 Pages: 1526-1548
  • Peer Reviewed
• [Journal Article] Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data (2009)
  • Author(s): Kozono, H., Yanagisawa, T.
  • Journal Title: Math.Z. 262 Pages: 27-39
  • Peer Reviewed
• [Journal Article] Global DIV-CURL Lemma in bounded domains in R^3 (2009)
  • Author(s): Kozono, H, Yanagisawa, T
  • Journal Title: Jour.Funct. Anal 256 Pages: 847-3859
  • Peer Reviewed
• [Journal Article] L^r-variational inequality for vector fields and the Helmholtz-Weyl decomposition in boundeddomains (2009)
  • Author(s): Kozono, H., Yanagisawa, T.
  • Journal Title: Indiana Univ.Math.J. 58 Pages: 1853-1920
  • Peer Reviewed
• [Presentation] Blow-up for a semilinear parabolic equation with large diffusion on R^N (2010)
  • Author(s): 石毛和弘
  • Organizer: 4^<th> Euro-Japanese Workshop on Blow-up
  • Place of Presentation: Lorentz Center, Leiden
  • Year and Date: 2010-09-10
• [Presentation] Leray's inequality in 3D multi-connected domains (2009)
  • Author(s): 小薗英雄
  • Organizer: Workshop on Mathematical Aspects of Hydrodynamics
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Ger many
  • Year and Date: 20090719-20090725
• [Presentation] Global Div-Curl Lemma in 3D bounded domains (2009)
  • Author(s): 小薗英雄
  • Organizer: International Conference on HarmonicAnalysis and Partial Differential Equations with Applications
  • Place of Presentation: Beijing Normal University(Beijing, China)
  • Year and Date: 20090526-20090530
• [Presentation] Leray's inequality in 3D domains (2009)
  • Author(s): 小薗英雄
  • Organizer: International Conference on Parabolic Equations2009 : On the occasion of Prof.Herbert Amann's 70h birthday
  • Place of Presentation: Banach Center(Bedlewo, Poland)
  • Year and Date: 20090511-20090515
• [Presentation] Global Div-Curl Lemma in 3D bounded domains (2009)
  • Author(s): 小薗英雄
  • Organizer: German-Japanese International Trainning Groups Waseda-Darmstadt University Mathematical Fluid Dynamics Launching Workshop
  • Place of Presentation: 早稲田大学
  • Year and Date: 20090414-20090416
• [Remarks] ホームページ
  • URL: http://www.math.tohoku.ac.jp/researchfields/kozono.html