On the Cauchy problem for a nonlinear Sobolev type equation

被引：2

作者：

Aristov, A. I. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow, Russia

来源：

DIFFERENTIAL EQUATIONS | 2014年 / 50卷 / 01期

关键词：

Differential Equation; Initial Data; Cauchy Problem; Asymptotic Expansion; Linear Part;

D O I：

10.1134/S0012266114010157

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the large-time asymptotics of the solution of the Cauchy problem for a nonlinear Sobolev type equation. We show that if initial data are sufficiently small in some norm, then the leading term of the asymptotic expansion is determined by the linear part of the equation and has exponential character, while the nonlinearity affects the decay order of the remainder.

引用

页码：117 / 121

页数：5