H−perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation
نویسندگان
چکیده
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 [8] are included in the analysis.
منابع مشابه
Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.
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