The invariant region for the equations of nonisentropic gas dynamics

Abstract

We study the existence of the invariant region for the equations of nonisentropic gas dynamics. We obtain the mean-integral of the conserved quantity after making an intensive study of the Riemann problem. Using the extremum principle and the Lagrangian multiplier method, we prove that the one-dimensional equations of nonisentropic gas dynamics for an ideal gas possess a unique invariant region. However, the invariant region is not bounded. doi:10.1017/S144618111600033X