Abstract

We consider a one-dimensional (1D) piston problem for the Zeldovich-von Neumann-Döring (ZND) combustion model with a one-step exothermic chemical reaction. This problem can be seen as a Riemann initial-boundary value problem. In order to construct a detonation wave solution to the piston problem, we consider a free boundary value problem for the ZND model. Existence of global in time classical solution to this free boundary value problem is obtained by the method of characteristics, providing that the binding energy q is sufficiently small.

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