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

TL;DR

This paper proves the global existence of detonation wave solutions in a free boundary problem for the ZND combustion model without dissipation conditions, advancing understanding of shock wave behavior.

Contribution

It establishes the existence of detonation waves in a free boundary setting for the ZND model without requiring dissipation assumptions, which was not previously shown.

Findings

Proves global existence of detonation wave solutions.

Models detonation as a free boundary problem.

Removes dissipation conditions from previous analyses.

Abstract

In this paper, we study detonation wave solutions to one-dimensional piston problem for the Zeldovich-von Neumann-D{\"o}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.