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

Abstract

This article studies a Riemann problem for the so-called “[Formula: see text]-system”[Formula: see text], [Formula: see text], 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 [Formula: see text] as an entire function that takes real values on the real axis, this product also extends for certain distributions [Formula: see text] the meaning of [Formula: see text]. Under certain conditions, this Riemann problem has solutions that are [Formula: see text]-shock waves. Furthermore, those [Formula: see text]-shock waves satisfy the so-called generalized Rankine–Hugoniot conditions.