Global solutions and blow-up phenomena for the periodic b-equation

被引：17

作者：

Zhang, S. ^{[1
]}

Yin, Z. ^{[1
]}

机构：

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

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 82卷

关键词：

DEGASPERIS-PROCESI EQUATION; SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; KORTEWEG-DEVRIES EQUATION; WELL-POSEDNESS; INTEGRABLE EQUATION; PEAKON SOLUTIONS; WEAK SOLUTIONS; CAUCHY-PROBLEM; WAVE SOLUTIONS;

D O I：

10.1112/jlms/jdq044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper, we mainly study the Cauchy problem of a family of asymptotically equivalent shallow water wave equations, the so called periodic b-equation. We first establish the local well-posedness for the periodic b-equation. Then we derive the precise blow-up scenario and present two blow-up results. Moreover, we show that the periodic b-equation has global strong solutions. Finally, we prove the existence of global weak solutions to the periodic b-equation, provided that initial data satisfy certain sign conditions.

引用

页码：482 / 500

页数：19

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