On the Cauchy problem for the periodic b-family of equations and of the non-uniform continuity of Degasperis-Procesi equation

被引：39

作者：

Christov, Ognyan ^{[2
]}

Hakkaev, Sevdzhan ^{[1
]}

机构：

[1] Univ Shumen, Fac Math & Informat, Shumen 9712, Bulgaria

[2] Univ Sofia, Fac Math & Informat, Sofia 1164, Bulgaria

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 360卷 / 01期

关键词：

Blow-up; Uniform continuity; Camassa-Holm equation; SHALLOW-WATER EQUATION; BLOW-UP PHENOMENA; CAMASSA-HOLM; GLOBAL EXISTENCE; BREAKING WAVES; WELL-POSEDNESS; ILL-POSEDNESS;

D O I：

10.1016/j.jmaa.2009.06.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of the existence of the global solutions and formation of singularities for a b-family of equations which includes the Camassa-Holm and Degasperis-Procesi equation. We also consider the problem of the uniformly continuity of Degasperis-Procesi equation. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：47 / 56

页数：10

共 25 条

[11] Non-uniform continuity of periodic Holm-Staley b-family of equations
Christov, Ognyan
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[12] Non-uniform dependence on initial data for the generalized Degasperis-Procesi equation on the line
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[13] The Cauchy Problem for a Dissipative Periodic 2-Component Degasperis-Procesi System
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[14] Non-uniform dependence for a generalized Degasperis–Procesi equation
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[16] A rigidity result for the Holm-Staley b-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakon
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[17] On the Cauchy Problem for the b-Family Equations with a Strong Dispersive Term
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JOURNAL OF APPLIED MATHEMATICS, 2011,
[18] The local well-posedness in Besov spaces and non-uniform dependence on initial data for the interacting system of Camassa-Holm and Degasperis-Procesi equations
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[19] Non-uniform continuity on initial data for the two-component b-family system in Besov space
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MONATSHEFTE FUR MATHEMATIK, 2023, 201 (02): : 547 - 563
[20] Non-uniform continuity on initial data for the two-component b-family system in Besov space
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