Wave-Front Tracking for the Equations of Non-Isentropic Gas Dynamics

We study the model equations of polytropic gas dynamics, which constitute a system of three hyperbolic conservation laws. Global in time BV-solutions were obtained by T.-P. Liu (Indiana Univ. Math. J.,1978) provided that $(gamma - 1)$ times the total variation of the initial data is sufficiently small; here $gamma$ is the adiabatic coefficient. The aim of this paper is to give an alternative proof by exploiting the Dafermos-Bressan-Risebro wave-front tracking scheme. An original feature is the use of the path decomposition method to obtain pathwise estimates of the approximate solutions; these estimates show the decay properties of the solutions and play a crucial role in proving the stability of the wave-front tracking scheme.