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.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | All Preprints | Preprint Server Homepage ]

Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Wed Oct 26 09:59:08 MEST 2005