PERSISTENCE PROPERTIES AND INFINITE PROPAGATION FOR THE MODIFIED 2-COMPONENT CAMASSA-HOLM EQUATION

被引：11

作者：

Wu, Xinglong ^{[1
]}

Guo, Boling ^{[1
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 07期

关键词：

The modified 2-component Camassa-Holm equation; persistence properties; compact support; exponential decay; infinite propagation speed; SHALLOW-WATER EQUATION; CONSERVATIVE SOLUTIONS; BREAKING WAVES;

D O I：

10.3934/dcds.2013.33.3211

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we mainly study persistence properties and infinite propagation for the modified 2-component Camassa-Holm equation. We first prove that persistence properties of the solution to the equation provided the initial potential satisfies a certain sign condition. Finally, we get the infinite propagation if the initial datas satisfy certain compact conditions, while the solution to system (1.1) instantly loses compactly supported, the solution has exponential decay as vertical bar x vertical bar goes to infinity.

引用

页码：3211 / 3223

页数：13

共 22 条

[1] Multi-peakons and a theorem of Stieltjes [J].

Beals, R ;

Sattinger, DH ;

Szmigielski, J .

INVERSE PROBLEMS, 1999, 15 (01) :L1-L4

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

Bressan, Alberto ;

Constantin, Adrian .

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

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

Bressan, Alberto ;

Constantin, Adrian .

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

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

CAMASSA, R ;

HOLM, DD .

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

[5]

Camassa R., 1994, Advances in Applied Mechanics, V31, P1

[6]

Constantin A, 2000, COMMUN PUR APPL MATH, V53, P603

[7] Finite propagation speed for the Camassa-Holm equation [J].

Constantin, A .

JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (02)

[8] 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

[9] On the blow-up rate and the blow-up set of breaking waves for a shallow water equation [J].

Constantin, A ;

Escher, J .

MATHEMATISCHE ZEITSCHRIFT, 2000, 233 (01) :75-91

[10] 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-+

← 1 2 3 →