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Delta Shock Wave for the Suliciu Relaxation System

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  • Richard De la cruz
  • Juan Galvis
  • Juan Carlos Juajibioy
  • Leonardo Rendón

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.

Suggested Citation

  • Richard De la cruz & Juan Galvis & Juan Carlos Juajibioy & Leonardo Rendón, 2014. "Delta Shock Wave for the Suliciu Relaxation System," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-11, June.
    • Handle: RePEc:hin:jnlamp:354349
    DOI: 10.1155/2014/354349
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