UMEDA, Noriaki:COE Researcher,Analysis

Keyword(s):
reaction-diffusion, heat equation, parabolic, system, blow-up, global, uniqueness, asymptotic behavior
Research Interest:
Solution of reaction-diffusion equation
Research Activities:
I studied blow-up in finite time, global existence and uniqueness of solution, and asymptotic behavior of these case. Research of this field was begun from Fujita in 1966, it is damaged by a lot of people, and researches various even now are done. Recently, we are interested in blow-up, global existence amd uniqueness of solution when performing diversification and generalization of an equation especially, and the relation between these phenomenon, and the form and the size of initial value, and the width and the form of a domain defined for the equation equations of a phenomenon and an initial value are defined. Paper-list:1. Blow-up and large time behavior of solutions of a weakly coupled system of reaction-diffusion equations Tsukuba J. Math. 27 (2003), 31-46. 2. Large Time Behavior and Uniqueness of Solutions of a Weakly Coupled System of Reaction-Diffusion Equations (to appear in Tokyo J. Math.). 3. Existence, Nonexistence of global solution and large time behavior of solutions of a weakly coupled system of reaction-diffusion equations (submitted).