Blow-up phenomena and persistence property for the modified b-family of equations

被引：3

作者：

Wang, Ying ^{[1
]}

Zhu, Min ^{[2
]}

机构：

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Peoples R China

[2] Nanjing Forestry Univ, Dept Math, Nanjing 310037, Jiangsu, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 03期

关键词：

Modified b-family of equations; Blow-up; Persistence; Weighted space; SHALLOW-WATER EQUATION; GLOBAL EXISTENCE; WELL-POSEDNESS; WAVE-BREAKING; SHOCK-WAVES; STABILITY; PEAKONS; TRAJECTORIES; DYNAMICS; SOLITONS;

D O I：

10.1016/j.jde.2016.09.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the blow-up mechanism and persistence property of solutions to the modified b-family of equations. The dynamics of the blow-up quantity along the characteristics is established by the Riccati-type differential inequality with various parameters. The key feature of the method is to refine the analysis on the growth rate of the relative ratio between solution and its gradient by performing a vertical shift. Furthermore, the persistence results for the solution are established in weighted spaces. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1161 / 1191

页数：31

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