Riemann Problem for a limiting system in elastodynamics

TL;DR

This paper analyzes the Riemann problem for a degenerate 2x2 system in elastodynamics, focusing on the limiting behavior as a parameter approaches zero, which connects to hyperbolic systems in the field.

Contribution

It introduces a method to solve the Riemann problem for a nonconservative, degenerate system and explores its relation to hyperbolic elastodynamics models.

Findings

Solution framework for the degenerate system's Riemann problem

Connection established between the limiting system and hyperbolic elastodynamics models

Insights into the behavior of solutions as the parameter tends to zero

Abstract

In this article, we discuss about the resolution of the Riemann problem for a 2x2 system in nonconservative form exhibiting parabolic degeneracy. The system can be perceived as the limiting equation (depending on a parameter tending to 0) of a 2x2 strictly hyperbolic, genuinely nonlinear, non-conservative system arising in context of a model in elastodynamics.