## 留言板

 引用本文: 曹镇潮, 陈彭年. 一类渗流方程解在边界上的不稳定性和Blow-up[J]. 应用数学和力学, 2005, 26(12): 1487-1492.
CAO Zhen-chao, CHEN Peng-nian. Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1487-1492.
 Citation: CAO Zhen-chao, CHEN Peng-nian. Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1487-1492.

## 一类渗流方程解在边界上的不稳定性和Blow-up

###### 作者简介:曹镇潮(1946- ),男,福建人,教授,硕士(联系人.Tel:+86-592-2181807;Fax:+86-592-2183209;E-mail:caozhen@xmu.edu.cn)
• 中图分类号: O175.26；O357.30

## Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation

• 摘要: 对一类具有非线性第二、第三边值条件的非线性渗流方程,证明了解的先验的界可以用初值和解在区域边界上的积分来估计和控制．这一先验估计是通过迭代技巧来建立的．根据这个估计,解可能在边界上爆破(Blow-up)从而解有渐近不稳定性．
•  [1] Rothe F.Uniform bounds from bounded L-functionals in reaction-diffusion equations[J].J Differential Equations,1982,45(2):207—233. [2] Friedman A,Lacey A A.Blow up of solutions of semilinear parabolic equations[J].J Math Anal Appl,1988,132(1):171—186. [3] Friedman A Mcleod B.Blow-up of positive solutions of semilinear heat equations[J].Indian Univ Math J,1985,34(2):425—447. [4] Gomez Lope J,Marquez V,Wolanski N.Blow-up results and localization of blow up points for the heat equation with a nonlinear boundary condition[J].J Differential Equations,1991,92(2):384—401. [5] Alikakos N D.An application of the invariance principle to reaction-diffusion equations[J].J Differential Equations,1979,33(2):201—225. [6] CAO Zhen-chao,GU Lian-kun.Initial-boundary value problem for a degenerate quasilinear parabolic equation of order 2m[J].J Partial Differential Equations,1990,3(1):13—20. [7] Ladyzenskaja O A,Solonnikov V A,Uralceva N N.Linear and Quasilinear Equations of Parabolic Type[M].AMS Translations of Mathematical Monographs,Vol 23,Rhode Island:AMS,1968. [8] Levin H A.Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time[J].J Differential Equations,1974,16(2):319—334.
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##### 出版历程
• 收稿日期:  2003-05-17
• 修回日期:  2005-05-31
• 刊出日期:  2005-12-15

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