Sammendrag
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 $H^1({\mathbb R})$. In particular, the supersonic solitary shock waves [8] are included in the analysis.