Global weak solutions to a generalized hyperelastic-rod wave equation

被引：140
作者：
Coclite, GM
Holden, H
Karlsen, KH
机构：
[1] Univ Oslo, Ctr Math Applicat, NO-0316 Oslo, Norway
[2] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2005年 / 37卷 / 04期
关键词：
hyperelastic-rod wave equation; Camassa-Holm equation; weak solutions; existence; uniqueness;
D O I：
10.1137/040616711
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa-Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H-1(R). We also present a "weak equals strong" uniqueness result.
引用
收藏
页码：1044 / 1069
页数：26
相关论文
共 38 条
[1]  
[Anonymous], 2001, ANALYSIS
[2]   Acoustic scattering and the extended Korteweg-de Vries hierarchy [J].
Beals, R ;
Sattinger, DH ;
Szmigielski, J .
ADVANCES IN MATHEMATICS, 1998, 140 (02) :190-206
[3]   MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS [J].
BENJAMIN, TB ;
BONA, JL ;
MAHONY, JJ .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) :47-+
[4]   AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].
CAMASSA, R ;
HOLM, DD .
PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664
[5]  
Coclite GM, 2005, DISCRETE CONT DYN-A, V13, P659
[6]   On the Cauchy problem for a family of quasilinear hyperbolic equations [J].
Constantin, A ;
Escher, J .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1998, 23 (7-8) :1449-1458
[7]   Wave breaking for nonlinear nonlocal shallow water equations [J].
Constantin, A ;
Escher, J .
ACTA MATHEMATICA, 1998, 181 (02) :229-243
[8]  
Constantin A, 1999, COMMUN PUR APPL MATH, V52, P949, DOI 10.1002/(SICI)1097-0312(199908)52:8<949::AID-CPA3>3.0.CO
[9]  
2-D
[10]   Global weak solutions for a shallow water equation [J].
Constantin, A ;
Molinet, L .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 211 (01) :45-61
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