Classification by the matrix representing the nonlinearity of the blowing up solutions for a reaction-diffusion system

• Project/Area Number: 23740129
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Waseda University
• Principal Investigator: YAMAUCHI Yusuke 早稲田大学, 重点領域研究機構, 研究員 (00451435)
• Project Period (FY): 2011 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 非線形偏微分方程式 / 非線形放物型方程式 / 解の爆発 / 反応拡散方程式

Research Abstract

We study the critical exponent of the blowing up of the solution for a reaction-diffusion system and the life span of the solution for a reaction-diffusion equation. The objective of the study is to understand the mechanism of the blowing up of the solution. In this study, we employ the matrix representing the nonlinearity of the equations. The matrix makes the analysis simple, and helps us to understand the mechanism of the blowing up.

Research Products

• [Journal Article] Life span of positive solutions for the Cauchy problem for the parabolic equations. (2012)
  • Author(s): Yusuke Yamauchi
  • Journal Title: Int. J. Differ. Equ. Volume: 2012 Pages: 16-16
  • DOI: 10.1155/2012/417261
  • Peer Reviewed
• [Journal Article] Life span of solutions for a semilinear heat equation with initial data having positive limit inferior at infinity (2011)
  • Author(s): Y. Yamauchi
  • Journal Title: Nonlinear Anal Volume: 74 Issue: 15 Pages: 5008-5014
  • DOI: 10.1016/j.na.2011.04.064
  • Peer Reviewed
• [Presentation] Life span of positive solutions for the Cauchy Problem for the parabolic equations (2013)
  • Author(s): Y. Yamauchi
  • Organizer: The 5^<th> Nagoya Workshop on Differential Equations
  • Place of Presentation: 名古屋大学
  • Year and Date: 2013-03-13
• [Presentation] Life span of positive solutions for the Cauchy Problem for the parabolic equations (2013)
  • Author(s): Y. Yamauchi
  • Organizer: The 14^<th> Northeastern Symposium on mathematical Analysis
  • Place of Presentation: 東北大学
  • Year and Date: 2013-02-18
• [Presentation] Life span of positive solutions for the Cauchy problem for the parabolic equations (2013)
  • Author(s): Y. Yamauchi
  • Organizer: The 5th Nagoya Workshop on Differential Equations
  • Place of Presentation: 名古屋大学
  • Invited
• [Presentation] Life span of positive solutions for the Cauchy problem for the parabolic equations (2013)
  • Author(s): Y. Yamauchi
  • Organizer: The 14th Northeastern Symposium on Mathematical Analysis
  • Place of Presentation: 東北大学
  • Invited
• [Presentation] Life span of positive solutions for the Cauchy Problem for the parabolic equations (2012)
  • Author(s): Y. Yamauchi
  • Organizer: 2012年度日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-20
• [Presentation] Life span of positive solutions for a semilinear heat equation with nondecaying initial data (2012)
  • Author(s): Y. Yamauchi
  • Organizer: The 9^<th> AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Orlando, Florida, USA
  • Year and Date: 2012-07-03
• [Presentation] Life span of positive solutions for the Cauchy problem for the parabolic equations (2012)
  • Author(s): 山内 雄介
  • Organizer: 2012年度日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] Life span of positive solutions for a semilinear heat equation with nondecaying initial data (2012)
  • Author(s): Y. Yamauchi
  • Organizer: The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Hyatt Regency Grand Cypress, Orlando, Florida, USA
  • Invited
• [Presentation] Life span of positive solutions for a semilinear heat equation with nondecaying initial data (2011)
  • Author(s): Y. Yamauchi
  • Organizer: The 4^<th> Japanese-German International Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-12-01
• [Presentation] Life span of positive solutions for a semilinear heat equation with nondecaying initial data (2011)
  • Author(s): Y. Yamauchi
  • Organizer: RIMS研究集会非平衡非線形現象の解析-発展方程式の立場から-
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-10-24
• [Presentation] 無限遠方にて減衰しない初期値に対する熱方程式の解の爆発時刻に関する指向性を持つ評価 (2011)
  • Author(s): Y. Yamauchi
  • Organizer: 2011年度日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-30
• [Presentation] Life span of positive solutions for a semilinear heat equation with nondecaying initial data (2011)
  • Author(s): Y. Yamauchi
  • Organizer: One Forum, Two Cities : Aspect of Nonlinear PDEs
  • Place of Presentation: National Taiwan University
  • Year and Date: 2011-08-30
• [Presentation] Life span of positive solutions for a semilinear heat equation with nondecaying initial data (2011)
  • Author(s): Y. Yamauchi
  • Organizer: The 36^<th> Sapporo Symposium on Partial Differential Equations
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-08-23
• [Presentation] 山内 雄介 (2011)
  • Author(s): 無限遠方にて減衰しない初期値に対する熱方程式の解の爆発時刻に関する指向性を持つ評価
  • Organizer: 日本数学会2011年度秋季総合分科会
  • Place of Presentation: 信州大学
• [Presentation] Y. Yamauchi (2011)
  • Author(s): Life span of positive solutions for a semilinear heat equation with nondecaying initial data
  • Organizer: 第４回日独流体数学国際研究集会(招待講演)
  • Place of Presentation: 早稲田大学
• [Presentation] Y. Yamauchi (2011)
  • Author(s): Life span of positive solutions for a semilinear heat equation with nondecaying initial data
  • Organizer: RIMS 研究集会非平衡非線形現象の解析-発展方程式の立場から-(招待講演)
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Y. Yamauchi (2011)
  • Author(s): Life span of positive solutions for a semilinear heat equation with nondecaying initial data
  • Organizer: One Forum, Two Cities: Aspect of Nonlinear PDEs
  • Place of Presentation: National Taiwan University
• [Presentation] Y. Yamauchi (2011)
  • Author(s): Life span of positive solutions for a semilinear heat equation with nondecaying initial data
  • Organizer: The 36th Sapporo Symposium on Partial Differential Equations(招待講演)
  • Place of Presentation: 北海道大学