A splitted Godunov scheme for solving a system of elasticity in a nonconservative form (Q2782326)

This paper deals with the simplified system modeling elasticity in Eulerian coordinates, that is NEWLINE\[NEWLINE\begin{aligned}\partial_tu(x,t) &+u(x,t) \partial_x u(x,t)-\partial_x \sigma(x,t) \approx 0,\\ \partial_t \sigma(x,t) & +u(x,t) \partial_x\sigma (x,t)-k^2 \partial_xu(x,t) \approx 0, \end{aligned}\tag{1}NEWLINE\]NEWLINE which is a dynamic equation coupled with Hooke law, with \(u\) representing the velocity, \(\sigma\) the stress and \(k\) a positive fixed real number. Here the authors propose a new Godunov scheme to compute an approximate solution for (1). Moreover they compare their approach for decreasing initial data with the Colombeau-Le Roux scheme.NEWLINENEWLINEFor the entire collection see [Zbl 0978.00050].