Global weak solutions to a generalized hyperelastic-rod wave equation

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 pr...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 37; no. 4; pp. 1044 - 1069
Main Authors COCLITE, G. M, HOLDEN, H, KARLSEN, K. H
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 2005
Subjects
Applied mathematics
Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Water waves
Wave equation
35A05
35L05
existence
weak solutions
Semigroup
Camassa Holm equation
Hyperelastic-rod wave equation
Global solution
Hyperelastic rod
35G25
Weak solution
Strong uniqueness
uniqueness
Generalized equation
Weak uniqueness
Camassa-Holm equation
Non linear wave
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0036-1410
1095-7154
DOI:10.1137/040616711