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 $H^1(\R)$. In particular, the supersonic solitary shock waves \cite{Dai:2000} are included in the analysis.
H1-perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation / Bendahmane, M.; Coclite, Giuseppe Maria; Karlsen, K. H.. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - 3:3-4(2006), pp. 419-432. [10.1007/s00009-006-0088-4]
H1-perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation
COCLITE, Giuseppe Maria;
2006-01-01
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. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from $H^1(\R)$. In particular, the supersonic solitary shock waves \cite{Dai:2000} are included in the analysis.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
