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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 354349, 11 pages
http://dx.doi.org/10.1155/2014/354349
Research Article

Delta Shock Wave for the Suliciu Relaxation System

1School of Mathematics and Statistics, Universidad Pedagógica y Tecnológica de Colombia, Tunja, Colombia
2Department of Mathematics, Universidad Nacional de Colombia, Bogotá, Colombia

Received 13 March 2014; Accepted 27 May 2014; Published 18 June 2014

Academic Editor: Manuel De León

Copyright © 2014 Richard De la cruz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that model viscoelastic fluids. An important issue is that the considered system is such that every characteristic field is linearly degenerate. We show an explicit solution for the Cauchy problem with initial data in . We also study the Riemann problem for this system. Under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta-shock type solutions are established.