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. We fix a smooth solution and 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.
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