We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa--Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from $H^1(\R)$. In particular, the supersonic solitary shock waves \cite{Dai:2000} are included in the analysis.
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Titolo: | $H^1-$perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation |
Autori: | |
Data di pubblicazione: | 2006 |
Rivista: | |
Abstract: | We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa--Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from $H^1(\R)$. In particular, the supersonic solitary shock waves \cite{Dai:2000} are included in the analysis. |
Handle: | http://hdl.handle.net/11586/18701 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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