Stability of ZND detonations for Majda's model

TL;DR

This paper demonstrates the stability of ZND detonations in Majda's model by calculating the Lopatinski determinant, confirming stability across parameters and extending results to viscous detonations with small viscosity.

Contribution

It provides a direct calculation of the Lopatinski determinant for Majda's model, establishing stability results that extend to viscous detonations.

Findings

Lopatinski determinant has a single zero at the origin, indicating stability.

ZND detonations in Majda's model are stable for all parameters considered.

Viscous detonations are stable for sufficiently small viscosity.

Abstract

We evaluate by direct calculation the Lopatinski determinant for ZND detonations in Majda's model for reacting flow, and show that on the nonstable (nonnegative real part) complex half-plane it has a single zero at the origin of multiplicity one, implying stability. Together with results of Zumbrun on the inviscid limit, this recovers the result of RoqueJoffre-Vila that viscous detonations of Majda's model also are stable for sufficiently small viscosity, for any fixed detonation strength, heat release, and rate of reaction.