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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Dedicated to the memory of Professor Aldo Cossu
The research of K.H. Karlsen is supported by an Outstanding Young Investigators Award from the Research Council of Norway. The current address of G.M. Coclite is Department of Mathematics, University of Bari, Via E. Orabona 4, 70125 Bari, Italy
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Bendahmane, M., Coclite, G.M. & Karlsen, K.H. H1-perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation. MedJM 3, 419–432 (2006). https://doi.org/10.1007/s00009-006-0088-4
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DOI: https://doi.org/10.1007/s00009-006-0088-4