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.
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