A duality principle corresponding to the parabolic equations

被引：6
作者：
Il'yasov, Yavdat [1 ]
机构：
[1] Ufa State Aviat Tech Univ, Ufa, Russia
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2008年 / 237卷 / 05期
基金：
俄罗斯基础研究基金会;
关键词：
dual variational principle; nonlinearity indefinite in sign; blow-up;
D O I：
10.1016/j.physd.2007.10.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Our principal problem consists in finding threshold values for a family of blow-up solutions of nonlinear evolution problems depending on a real parameter;. We seek to obtain the solution of the problem in a constructive and unified approach which would provide the answer for the following general question: Is there is a constructive method for finding the threshold values? We illustrate our approach by means of an example of finding. a threshold value for a family of parabolic equations with nonlinearity indefinite in sign. In the main result, the threshold value is expressed via explicitly specified dual variational principles of a new type. (c) 2007 Elsevier B. V. All rights reserved.
引用
收藏
页码：692 / 698
页数：7
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