On the Blow-up of Solutions to Nonlinear Initial-Boundary Value Problems

被引：0
作者：
Pohozaev, S. I. [1 ]
机构：
[1] Russian Acad Sci, VA Steklov Math Inst, Moscow, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2008年 / 260卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
STEKLOV Institute; Nonlinear Problem; Global Solution; Nontrivial Solution; Nonlinear Operator;
D O I：
10.1134/S008154380801015X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the problem of nonexistence (blow-up) of solutions of nonlinear evolution equations in the case of a bounded (with respect to the space variables) domain. Following the method of nonlinear capacity based on the application of test functions that are optimal ("characteristic") for the corresponding nonlinear operators, we obtain conditions for the blow-up of solutions to nonlinear initial-boundary value problems. We also show by examples that these conditions are sharp in the class of problems under consideration.
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页码：204 / 217
页数：14
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