On one-dimensional shock waves

In this paper uniform asymptotic expansions for the solutions of a system of differential equations are obtained in the domain containing a shock wave. It is shown, in particular, that the function θ(t,x)/ε contained in the expansions and describing the behavior of the solution in the neighborhood of the wave front has, generally speaking, a discontinuity of derivatives at the front. The results are applicable to one-dimensional problems in gas dynamics with low viscosity and heat-conductivity.