Preprint 1997007
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 BVsolution 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.
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