The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations

CHEN Song-lin

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(11): 1217-1220

CHEN Song-lin. The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1217-1220.

Citation:

CHEN Song-lin. The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1217-1220.

Citation:

CHEN Song-lin. The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1217-1220.

PDF( 188 KB)

The Extinction Behavior of the Solutions for a Class of Reaction-Diffusion Equations

CHEN Song-lin

Department of Mathematics Physics, Aahui University of Techn ology, Ma'anshan, Anhui 243002, P R China

Received Date: 1999-12-14
Rev Recd Date: 2001-03-20
Publish Date: 2001-11-15

Abstract

Abstract

The methods of L^p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boudnary values A sufficient and a necessary condition about the extinction of the solutions is given.Here λ>0,γ>0,β>0 are constants,Ω⊂R^N is bounded with smooth boundary Ω.At last,it is simulated with a higher order equation by using the present methods.
- reaction-diffusion equation,
- extinction,
- L^p estimation,
- Bernoulli equation

FullText(HTML)

References(9)

References

[1]	Ladyzenska O A, Solonnikav V A, Vral'tseva N N. Linear and Quasilinear Equations of Parabolic Type[M]. Providence R I: Amer Math Soc,1968.
[2]	顾永耕. 抛物型方程的解熄灭(extinction)的充要条件[J]. 数学学报,1994,37(1):73-79.
[3]	Tsutsumi M. On solution of some doubly nonlinear degenerate parabolic equations with absorption[J]. J Math Anal Appl,1988,132(1):187-212.
[4]	蔡日增. 一类半线性抛物型方程的解熄灭现象[J]. 南京大学学报数学半年刊,1995,12(1):116-120.
[5]	Vladimir G M. Solbolev Spaces[M]. Berlin, Herdelberg, New York, Tokyo: Spring-Verlag,1995.
[6]	吉耳巴格 D, 塔丁格 N S. 二阶椭圆型偏微分方程[M]. 上海:上海科学技术出版社,1981.
[7]	Friedman A. Partial Differential Equations of Parabolic Type[M]. Fla: Krieger Malabar,1983.
[8]	Lin C S, Ni W M, Takagi I. Large amplitude stationary solutions to a chemotaxis system[J]. J Diff Eqns,1988,72(1):1-27.
[9]	陈松林. 一个反应扩散方程解的熄灭行为[J]. 数学研究与评论,1998,18(3):583-586.