New -shock waves in the -system: a distributional product approach

Abstract

This article studies a Riemann problem for the so-called “-system”, , which rules one-dimensional isentropic thermoelastic media. Such study is made using a product of distributions that allows us to extend both the classical solution concept and a weak solution concept. By considering as an entire function that takes real values on the real axis, this product also extends for certain distributions the meaning of . Under certain conditions, this Riemann problem has solutions that are -shock waves. Furthermore, those -shock waves satisfy the so-called generalized Rankine–Hugoniot conditions.