Blowup of solutions of a Korteweg-de Vries-type equation

被引：3
|
作者：
Yushkov, E. V. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2012年 / 172卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
Korteweg-de Vries-type equation; initial boundary value problem; solution blowup; global solvability;
D O I：
10.1007/s11232-012-0087-5
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We investigate the nonlinear third-order differential equation (u(xx) - u)(t) + u (xxx) + uu(x) = 0 describing the processes in semiconductors with a strong spatial dispersion. We study the problem of the existence of global solutions and obtain sufficient conditions for the absence of global solutions for some initial boundary value problems corresponding to this equation. We consider examples of solution blowup for initial boundary value and Cauchy problems. We use the Mitidieri-Pokhozhaev nonlinear capacity method.
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页码：932 / 938
页数：7
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