Existence of detonation wave solutions to the piston problem for the Zeldovich-von Neumann-D{ö}ring combustion model

Abstract

In this paper, we study detonation wave solutions to one-dimensional piston problem for the Zeldovich-von Neumann-D{ö}ring (ZND) combustion model with a one-step exothermic chemical reaction. As a special type of shock wave, the position of the detonation wave is unknown, which make our model to be a free boundary problem.~The global existence of detonation wave solutions to this free boundary problem is proved. Compared with previous result~\cite{Lai}, we do not impose any dissipation conditions on the equations and the boundaries.