Existence of detonation wave solutions to the piston problem for the Zeldovich-von Neumann-D{\"o}ring combustion model
Analysis of PDEs
2026-05-07 v1
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.
Cite
@article{arxiv.2605.04836,
title = {Existence of detonation wave solutions to the piston problem for the Zeldovich-von Neumann-D{\"o}ring combustion model},
author = {Xiaomin Zhang and Huimin Yu},
journal= {arXiv preprint arXiv:2605.04836},
year = {2026}
}