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Existence and uniqueness theorems are established for initials-boundary value problems corresponding to the equaction under assumptions on P and a that include as special cases the isentropic gas law P(v) = v−γ with γ>1 with α(v) = v −1 along with generalizations that allow for Non convex P. The smoothness assumptions made on P and α are much weaker then are usual in studying these problems and the initial data is only required to satisfy
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