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

页码：63 / 79

页数：17

共 50 条

[41] Ribonucleotide Incorporation by Eukaryotic B-Family Replicases and Its Implications for Genome Stability
Williams, Jessica S.
Kunkel, Thomas A.
ANNUAL REVIEW OF BIOCHEMISTRY, 2022, 91 : 133 - 155
[42] Peakon Solutions of Alice-Bob b-Family Equation and Novikov Equation
Wang, Jing
Xiong, Na
Li, Biao
ADVANCES IN MATHEMATICAL PHYSICS, 2019, 2019
[43] EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS FOR RELATIVISTIC SINGULAR EQUATIONS
Chu, Jifeng
Liang, Zaitao
Liao, Fangfang
Lu, Shiping
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2017, 16 (02) : 591 - 609
[44] Blow-up issues for the weakly dissipative periodic b-family of equations revisited
Dong, Xiaofang
JOURNAL OF MATHEMATICAL PHYSICS, 2020, 61 (12)
[45] Non-uniform continuity of periodic Holm-Staley b-family of equations
Christov, Ognyan
Hakkaev, Sevdzhan
Iliev, Iliya D.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) : 4821 - 4838
[46] Invariant analysis and conservation laws of the time-fractional b-family peakon equations
Zhang, Zhi-Yong
Li, Guo-Fang
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 103
[47] Stability of solutions for a family of nonlinear difference equations
Sun, Taixiang
Xi, Hongjian
Han, Caihong
ADVANCES IN DIFFERENCE EQUATIONS, 2008, : 238068
[48] Stability of Singular Solutions of Nonlinear Equations with Restricted Smoothness Assumptions
Andreas Fischer
Alexey F. Izmailov
Mario Jelitte
Journal of Optimization Theory and Applications, 2023, 196 : 1008 - 1035
[49] Stability of Singular Solutions of Nonlinear Equations with Restricted Smoothness Assumptions
Fischer, Andreas
Izmailov, Alexey F.
Jelitte, Mario
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2023, 196 (03) : 1008 - 1035
[50] Diversity and evolution of B-family DNA polymerases
Kazlauskas, Darius
Krupovic, Mart
Guglielmini, Julien
Forterre, Patrick
Venclovas, Ceslovas
NUCLEIC ACIDS RESEARCH, 2020, 48 (18) : 10142 - 10156

← 1 2 3 4 5 →