Preprint 2005-040

H1-Perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-Rod Wave Equation

Mostafa Bendahmane, Giuseppe Maria Coclite, and Kenneth H. Karlsen

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 $H1(\R)$. In particular, the supersonic solitary shock waves \cite{Dai:2000} are included in the analysis.

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Mostafa Bendahmane, <>
Giuseppe Maria Coclite <>
Kenneth Hvistendahl Karlsen, <>
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<> October 18 2005.

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