Invariants and wave breaking analysis of a Camassa-Holm type equation with quadratic and cubic non-linearities

被引：18

作者：

Freire, Igor Leite ^{[1
]}

Sales Filho, Nazime ^{[2
,3
]}

de Souza, Ligia Correa ^{[2
,4
]}

Toffoli, Carlos Eduardo ^{[2
,4
]}

机构：

[1] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Ave Estados 5001, BR-09210580 Santo Andre, SP, Brazil

[2] Univ Fed ABC, Programa Posgrad Matemat, Ave Estados 5001, BR-09210580 Santo Andre, SP, Brazil

[3] Univ Fed Mato Grosso, Fac Engn, Av Fernando Correa da Costa 2367, BR-78060900 Cuiaba, MT, Brazil

[4] Inst Fed Educ Ciencia & Tecnol Sao Paulo, Campus Campos do Jordao, BR-12460000 Campos Do Jordao, SP, Brazil

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 08期

关键词：

Camassa-Holm type equations; Well-posedness; Wave breaking; Symmetries; Conservation laws; SHALLOW-WATER EQUATION; SYMBOLIC COMPUTATION; DEGASPERIS-PROCESI; CONSERVATION-LAWS; WELL-POSEDNESS; CAUCHY-PROBLEM; SYMMETRIES; STABILITY; INSTABILITY; EXISTENCE;

D O I：

10.1016/j.jde.2020.04.041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A non-local evolution equation of the Camassa-Holm type with dissipation is considered. The local well-posedness of the solutions of the Cauchy problem involving the equation is established via Kato's approach and the wave breaking scenario is also described. To prove such result, we firstly construct conserved currents for the equation and from them, conserved quantities. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：56 / 77

页数：22

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