Preprint 1997-007
On the zero relaxation limit for a system modeling the motions of a
viscoelastic solid
Wen Shen, Aslak Tveito, and Ragnar Winther
Abstract:
We consider a simple model of the motions of
a viscoelastic solid. The model consists of a two by two system of
conservation laws including a strong relaxation term.
We establish the existence of a BV-solution of this system for any
positive value of the relaxation parameter.
We also show that this solution is stable with respect to
the perturbations of the initial data in $L^1$.
By deriving the uniform bounds, with respect to the relaxation
parameter, on the total variation of the solution, we prove that the
solution converges towards the solution of a scalar conservation law
as the relaxation parameter goes to zero.
- Paper:
- Available as PostScript
- Title:
- On the zero relaxation limit for a system modeling the motions of a
viscoelastic solid
- Author(s):
- Wen Shen ,
<wens@ifi.uio.no>
- Aslak Tveito ,
<aslak@ifi.uio.no>
- Ragnar Winther ,
<ragnar@ifi.uio.no>
- Publishing information:
- Preprint, Department of Informatics, University of Oslo, 1997.
- Comments:
- Revised version received January 27 1998.
- Submitted by:
-
<wens@ifi.uio.no>
March 28 1997.
[
1996 Preprints
|
1997 Preprints
|
All Preprints
|
Preprint Server Homepage
]
© The copyright for the following
documents lies with the authors. Copies of these documents made by electronic
or mechanical means including information storage and retrieval systems, may
only be employed for personal use.
Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Wed Jan 28 09:26:36 1998