Preprint 1997-007

On the zero relaxation limit for a system modeling the motions of a viscoelastic solid

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 , mailto:wens@ifi.uio.no

Aslak Tveito , mailto:aslak@ifi.uio.no

Ragnar Winther , mailto:ragnar@ifi.uio.no

Publishing information:

Preprint, Department of Informatics, University of Oslo, 1997.

Comments:

Revised version received January 27 1998.

Submitted by:

mailto:wens@ifi.uio.no March 28 1997.