Delta Shock Wave for the Suliciu Relaxation System

Abstract EN

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.