Dissipative solutions for the modified two-component Camassa-Holm system

被引：2

作者：

Wang, Yujuan ^{[1
]}

Song, Yongduan ^{[1
]}

机构：

[1] Chongqing Univ, Sch Automat, Inst Smart Syst & Renewable Energy, Chongqing 400044, Peoples R China

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2014年 / 21卷 / 03期

基金：

中国国家自然科学基金;

关键词：

The modified two-component Camassa-Holm system; Global solutions; Dissipative solutions; Lagrangian variables; GLOBAL CONSERVATIVE SOLUTIONS; SHALLOW-WATER SYSTEM; BLOW-UP PHENOMENA; MULTIPEAKON SOLUTIONS; WAVE BREAKING; EQUATION; EXISTENCE;

D O I：

10.1007/s00030-013-0249-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Camassa-Holm model is capable of characterizing the dynamic behavior of shallow water wave, thus has been extensively studied. This paper is concerned with shallow water wave behavior after wave breaking. To better reflect the whole process, the modified two-component Camassa-Holm system is considered. The continuation of solutions of such system after wave braking is investigated. By introducing a skillfully defined characteristic, together with a set of newly defined variables, the original system is converted into a Lagrangian equivalent system, from which global dissipative solutions are obtained. The results obtained herein are deemed useful in understanding the dynamic behavior of shallow water wave during and after wave breaking.

引用

页码：339 / 360

页数：22

共 32 条

[1] Global dissipative solutions of the Camassa-Holm equation [J].

Bressan, Alberto ;

Constantin, Adrian .

ANALYSIS AND APPLICATIONS, 2007, 5 (01) :1-27

[2] Global conservative solutions of the Camassa-Holm equation [J].

Bressan, Alberto ;

Constantin, Adrian .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 183 (02) :215-239

[3] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[4] A two-component generalization of the Camassa-Holm equation and its solutions [J].

Chen, M ;

Liu, SQ ;

Zhang, YJ .

LETTERS IN MATHEMATICAL PHYSICS, 2006, 75 (01) :1-15

[5] Wave breaking for nonlinear nonlocal shallow water equations [J].

Constantin, A ;

Escher, J .

ACTA MATHEMATICA, 1998, 181 (02) :229-243

[6] On the scattering problem for the Camassa-Holm equation [J].

Constantin, A .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2008) :953-970

[7] Existence of permanent and breaking waves for a shallow water equation: A geometric approach [J].

Constantin, A .

ANNALES DE L INSTITUT FOURIER, 2000, 50 (02) :321-+

[8]

Constantin A., 1997, Expos. Math, V15, P53

[9] On an integrable two-component Camassa-Holm shallow water system [J].

Constantin, Adrian ;

Ivanov, Rossen I. .

PHYSICS LETTERS A, 2008, 372 (48) :7129-7132

[10] The Hydrodynamical Relevance of the Camassa-Holm and Degasperis-Procesi Equations [J].

Constantin, Adrian ;

Lannes, David .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 192 (01) :165-186

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