On Sobolev-type equations with critical nonlinearities

被引：0

作者：

Kaikina, E. I. ^{[1
]}

Naumkin, P. I. ^{[1
]}

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

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 119992, Russia

来源：

DOKLADY MATHEMATICS | 2006年 / 74卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.1134/S1064562406050140

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The large-time asymptotic behavior of the solutions to the Cauchy problem for the nonlinear Sobolev-type equation, is discussed. The considered Cauchy problem consists of critical nonlinearity for any spatial dimension n ≥1. The approach does not apply to higher dimensions as the lower estimate of the order of nonlinearity exceeds the critical value of σ = 1/n. An energy-type weighted a priori estimate for solutions is obtained to calculate the large-time asymptotics of the solutions.

引用

页码：672 / 675

页数：4

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