Stability of singular solutions to the b-family of equations

被引：0
|
作者：
Huang, Shou-Jun [1 ,2 ]
Wu, Li-Fan [2 ]
机构：
[1] Zhejiang Normal Univ, Coll Math Med, Jinhua 321004, Peoples R China
[2] Anhui Normal Univ, Dept Math, Wuhu 241002, Peoples R China
来源：
MONATSHEFTE FUR MATHEMATIK | 2024年 / 204卷 / 01期
关键词：
Shallow water wave equation; b-family of equation; Singular solution; Asymptotic stability; BLOW-UP PHENOMENA; SHALLOW-WATER EQUATION; CAMASSA-HOLM; WELL-POSEDNESS; ILL-POSEDNESS; ORBITAL STABILITY; GLOBAL-SOLUTIONS; SOLITARY WAVES; PEAKONS;
D O I：
10.1007/s00605-024-01964-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we first construct some explicit solutions to theb-family of equations,which will become unbounded in a finite time. Then, we investigate the asymptoticstability of the aforementioned singular solutions of the b-family of equations in theSobolev space H-s with s >(7)/(2). It is also interesting to point out that this stability highlydepends on the values of parameterb, that is, b is an element of (-1,2]. The proof is based on thedetailed analysis on the estimates of the perturbed solutions and the properties of thecorresponding linear operators.
引用
收藏
页码：63 / 79
页数：17
相关论文
共 50 条
12345