Preprint 2005-040

H1-Perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-Rod Wave Equation

Mostafa Bendahmane, Giuseppe Maria Coclite, and Kenneth H. Karlsen

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 $H1(\R)$. In particular, the supersonic solitary shock waves \cite{Dai:2000} are included in the analysis.


Paper:
Available as PDF (216 Kbytes).
Author(s):
Mostafa Bendahmane, <mostafab@math.uio.no>
Giuseppe Maria Coclite <giusepc@math.uio.no>
Kenneth Hvistendahl Karlsen, <kennethk@math.uio.no>
Publishing information:
Comments:
Submitted by:
<giusepc@math.uio.no> October 18 2005.


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