Stability of ZND detonations for Majda's model

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.

This is the same as the paper published in Quart. Appl. Math. 70 (2012), with minor fix. We allow u_+ \geq 0(not only u_+=0) that was mistakenly omitted in original treatment. The analogy of the model for gas dynamics is only for u_+ \geq 0, the "physical" range defined by Majda