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.
$H^1-$perturbations of smooth solutions for a weakly dissipative hyperelastic-rod wave equation
COCLITE, Giuseppe Maria;
2006-01-01
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.File in questo prodotto:
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