Front instability in a condensed phase combustion model

Abstract

We consider a condensed phase (or solid) combustion model and its linearization around the travelling front solution. We construct an Evans function to characterize the eigenvalues of the linearized problem. We estimate this functional in the high activation energy limit. We deduce the existence of zeros with nonnegative real part for high activation energy, which proves the linear instability of the travelling front solution.

Keywords

• reaction-diffusion system
• travelling wave
• solid combustion
• linear instability
• evans function
• 35b35
• 35k55
• 35k57
• 35p15