THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

被引：0

作者：

林支桂

谢春红

王明新

机构：

来源：

ActaMathematicaScientia | 1998年 / 04期

关键词：

parabolic system; blow-up rate; blow-up set;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

This paper deals with the blow-up properties of solutions to the systems u_t Δu=ev（x0,t）, v_t-Δv=e（x0,t） in Ω×（0,T） subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.

引用

页码：413 / 420

页数：8

共 7 条

[1]

The blow-up property of solution to some differential equations with noulocal noalinear reaction. Chadam J M,Piece A,Yin H M. Journal of Mathematical Analysis and Applications . 1992

[2]

Total blowup versus single point blow-up. Bebernes J,Bressan A,Lacey A. Journal of Differential Equations . 1988

[3]

Lacey A A, Wake G C.Steady states of reaction-diffusion equations. Bruneell J G. Journal of the Australian Mathematical Society . 1983

[4]

The asymptotic behavior of blowup solution of localized nonlinear equation. Wang L W,Chen Q Y. Journal of Mathematical Analysis and Applications . 1996

[5]

A semilinear parabolic system in a bounded domain[J] . M. Escobedo,M. A. Herrero. &nbspAnnali di Matematica Pura ed Applicata . 1993 (1)

[6]

Nonlinear Parabolic and Elliptic Equations. Pao C V. . 1992

[7]

Boundedness and blow-up for a semilinear reacting diffusion system. Escobedo M,Herrero M A. Journal of Differential Equations . 1991

← 1 →