# 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).