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We study the model equations of polytropic gas\uddynamics, which constitute a system of three hyperbolic conservation laws. Global in time BV-solutions were obtained by T.-P. Liu (Indiana Univ. Math. J.,\ud1978) provided that $(\gamma - 1)$ times the total variation of\udthe initial data is sufficiently  small; here $\gamma$ is the adiabatic coefficient. The aim of this paper is\udto give an alternative proof by exploiting the\udDafermos-Bressan-Risebro wave-front tracking scheme. An original\udfeature is the use of the path decomposition method to\udobtain pathwise estimates of the approximate solutions; these\udestimates show the decay properties of the solutions and play a\udcrucial role in proving the stability of the wave-front tracking\udscheme

Wave-front tracking for the equations of non-isentropic gas dynamics