Abstract
This paper is the first of a series aimed at deriving uniform stability results for strong ZND – Zeldovich–Neumann–Döring – 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.
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