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.
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页码：382 / 396
页数：15
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