On the zero relaxation limit for a system modeling the motions of a
Wen Shen, Aslak Tveito, and Ragnar Winther
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.
- Available as PostScript
- On the zero relaxation limit for a system modeling the motions of a
- Wen Shen ,
- Aslak Tveito ,
- Ragnar Winther ,
- Publishing information:
- Preprint, Department of Informatics, University of Oslo, 1997.
- Revised version received January 27 1998.
- Submitted by:
March 28 1997.
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