Weighted identities for solutions of generalized Korteweg-de Vries equations

被引：5

作者：

Pokhozhaev, S. I. ^{[1
]}

机构：

[1] Russian Acad Sci, VA Steklov Math Inst, Moscow 117901, Russia

来源：

MATHEMATICAL NOTES | 2011年 / 89卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

Korteweg-de Vries equation; initial boundary-value problem; weighted differential inequality; weighted integral inequality; blow-up of solutions; Holder's inequality; Young's inequality; Dirichlet boundary condition;

D O I：

10.1134/S0001434611030102

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the Korteweg-de Vries equation u (t) + u (xxx) + uu (x) = 0 and its generalization u (t) + u (xxx) + f(u)x = 0. For the solutions of these equations, weighted identities (differential and integral) are obtained. These identities make it possible to establish the blow-up (in finite time) of the solutions of certain boundary-value problems.

引用

页码：382 / 396

页数：15

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