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
收藏
页码：672 / 675
页数：4
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