A study of the global structure of interface dynamics and traveling waves in nonlinear diffusion equations

Research Project

Project/Area Number	23540254
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Global analysis
Research Institution	Kyoto Sangyo University
Principal Investigator	YAGISITA Hiroki 京都産業大学, 理学部, 教授 (80349828)
Project Period (FY)	2011-04-28 – 2016-03-31
Project Status	Completed (Fiscal Year 2015)
Budget Amount *help	¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000) Fiscal Year 2015: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000) Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000) Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000) Fiscal Year 2012: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000) Fiscal Year 2011: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Keywords	非線形現象 / 非線形解析 / 拡散方程式 / 非線形拡散系
Outline of Final Research Achievements	We researched on the linear heat equation underlying the study of systems of nonlinear diffusion equations and showed that, in the linear heat equation on the one-dimensional hole line, the details of irregular long-time behaviors such as has been reported in the KPP-Fisher equation and the semi-linear heat equation of Fujita type with super ciritical exponent. Furthermore, we researched on conditions for similar irregular long-time behaviors as ones revealed in the linear equation.