H1-perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation

• Autores: Mostafa Bendahmane, Giuseppe Maria Coclite, Kenneth H. Karlsen
• Localización: Mediterranean journal of mathematics, ISSN 1660-5446, Vol. 3, Nº. 3-4, 2006, págs. 419-432
• Idioma: inglés
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• Resumen

  • We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa¿Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. We fix a smooth solution and establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from In particular, the supersonic solitary shock waves [8] are included in the analysis.