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We consider the Cauchy problems of a non-strictly hyperbolic system whichdescribes the compressible Euler fluid with exothermic reaction. In this papera Lyapunov-type functional is constructed for balance laws. By analysis of theflow generated by front tracking method, we prove the well-posedness theoremsand present the local features of global solutions.

Stability and Uniqueness of Global Solutions to Euler Equations with Exothermic Reaction