Construction of higher order asymptotic expansions of solutions for nonlinear diffusion equations and its application

2016 Fiscal Year Final Research Report

• Project/Area Number: 24740107
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Osaka Prefecture University
• Principal Investigator: Kawakami Tatsuki 大阪府立大学, 工学(系)研究科(研究院), 准教授 (20546147)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 非線形拡散方程式 / 高次漸近展開 / 非線形積分方程式 / 分数冪拡散方程式 / 消散項付き波動方程式 / 動的境界条件

Outline of Final Research Achievements

We consider the integral equation with respect to nonlinear diffusion equations, which are represented by semilinear heat equations, in the whole space. Under the condition that solutions of nonlinear integral equations behave like a multiple of the integral kernel asymptotically, we established the method of obtaining the higher order linear asymptotic expansions, which depends on the degree of moment of initial data, and nonlinear asymptotic expansion, which depends on the conditions for the nonlinear term. Furthermore, we applied our arguments to the heat equation with nonlinear boundary condition on the half space, nonlinear damped wave equations in the whole space and fractional diffusion equations in the whole space.

Free Research Field

数物系科学