BLOW-UP AND DECAY OF THE SOLUTION OF THE WEAKLY DISSIPATIVE DEGASPERIS-PROCESI EQUATION

被引：48

作者：

Wu, Shuyin ^{[1
]}

Yin, Zhaoyang ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Dept Comp Sci, Guangzhou 510275, Guangdong, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2008年 / 40卷 / 02期

关键词：

the weakly dissipative Degasperis-Procesi equation; blow-up; blow-up rate; global strong solutions; decay of solutions;

D O I：

10.1137/07070855X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we mainly study several problems on the weakly dissipative Degasperis Procesi equation. We first establish the local well-posedness of the equation, derive a precise blow-up scenario, and present two blow-up criteria for strong solutions to the equation. We then give the precise blow-up rate of blow-up solutions to the equation. We finally prove that the equation has global strong solutions and these global solutions decay to zero as time goes to infinity provided the potentials associated with their initial data are of one sign.

引用

页码：475 / 490

页数：16

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