Delta Shock Wave for the Suliciu Relaxation System

Delta Shock Wave for the Suliciu Relaxation System

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...

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Main Authors: Richard De la cruz, Juan Galvis, Juan Carlos Juajibioy, Leonardo Rendón
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2014/354349
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spelling doaj-38dfdc1b6fe648f1b26200332fd4fef72021-07-02T04:05:25ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/354349354349Delta Shock Wave for the Suliciu Relaxation SystemRichard De la cruz0Juan Galvis1Juan Carlos Juajibioy2Leonardo Rendón3School of Mathematics and Statistics, Universidad Pedagógica y Tecnológica de Colombia, Tunja, ColombiaDepartment of Mathematics, Universidad Nacional de Colombia, Bogotá, ColombiaDepartment of Mathematics, Universidad Nacional de Colombia, Bogotá, ColombiaDepartment of Mathematics, Universidad Nacional de Colombia, Bogotá, ColombiaWe 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 3×3 system is such that every characteristic field is linearly degenerate. We show an explicit solution for the Cauchy problem with initial data in L∞. 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.http://dx.doi.org/10.1155/2014/354349
collection DOAJ
language English
format Article
sources DOAJ
author Richard De la cruz
Juan Galvis
Juan Carlos Juajibioy
Leonardo Rendón
spellingShingle Richard De la cruz
Juan Galvis
Juan Carlos Juajibioy
Leonardo Rendón
Delta Shock Wave for the Suliciu Relaxation System
Advances in Mathematical Physics
author_facet Richard De la cruz
Juan Galvis
Juan Carlos Juajibioy
Leonardo Rendón
author_sort Richard De la cruz
title Delta Shock Wave for the Suliciu Relaxation System
title_short Delta Shock Wave for the Suliciu Relaxation System
title_full Delta Shock Wave for the Suliciu Relaxation System
title_fullStr Delta Shock Wave for the Suliciu Relaxation System
title_full_unstemmed Delta Shock Wave for the Suliciu Relaxation System
title_sort delta shock wave for the suliciu relaxation system
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2014-01-01
description 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 3×3 system is such that every characteristic field is linearly degenerate. We show an explicit solution for the Cauchy problem with initial data in L∞. 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.
url http://dx.doi.org/10.1155/2014/354349
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AT juangalvis deltashockwaveforthesuliciurelaxationsystem
AT juancarlosjuajibioy deltashockwaveforthesuliciurelaxationsystem
AT leonardorendon deltashockwaveforthesuliciurelaxationsystem
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