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

Mostafa Bendahmane, Giuseppe Maria Coclite, Kenneth H. Karlsen

• 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.