A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions

被引：49
|
作者：
El Soufi, A.
Jazar, M.
Monneau, R.
机构：
[1] Univ Tours, CNRS, UMR 6083, Lab Math & Phys Theor, F-37200 Tours, France
[2] Lebanese Univ, Dept Math, Beirut, Lebanon
[3] Ecole Natl Ponts & Chaussees, CERMICS, F-77455 Marne La Vallee 2, France
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2007年 / 24卷 / 01期
关键词：
semi-linear parabolic equations; blow-up; global existence; asymptotic behavior of solutions; Gamma convergence; Neumann Heat kernel; non-local term; comparison principle;
D O I：
10.1016/j.anihpc.2005.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study a simple non-local semilinear parabolic equation in a bounded domain with Neumann boundary conditions. We obtain a global existence result for initial data whose L-infinity-norm is less than a constant depending explicitly on the geometry of the domain. A natural energy is associated to the equation and we establish a relationship between the finite-time blow up of solutions and the negativity of their energy. The proof of this result is based on a Gamma-convergence technique. (C) 2006 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：17 / 39
页数：23
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