Stability of ZND detonation waves in the Majda combustion model

This paper is the first of a series aimed at deriving uniform stability results for strong ZND - Zeldovich-Neumann-Doring - detonation waves, in the context of singular perturbations. In this work, the Majda and Majda-Rosales models with small viscosity are examined, and a dispersion relation accounting for the linear stability of the wave is derived, by means of matched asymptotics. A rigorous justification follows, in which the main difficulty is a uniform spectral estimate.