Steve Schecter, North Carolina State University

Stability of fronts in gasless combustion

Friday September 21st, 4pm, Phillips 332
(refreshments served in Phillips 330 starting at 3:30)

Abstract: For gasless combustion in one space dimension, we study stability of the combustion front with smallest wave speed. An appropriate notion of stability in this case is "convective stability," i.e., we allow only perturbations that decrease exponentially ahead of the front. These perturbations include the physically realistic initial conditions. Unfortunately, the linearized operator is not sectorial. Nevertheless, we show that the combustion front is nonlinearly stable provided the linearized operator has no eigenvalues in the right half-plane other than a simple eigenvalue at 0. Then we show by an Evans function calculation that the 0 eigenvalue, which traveling waves always have, is in fact simple. Finally, we present a numerical Evans function calculation that indicates that, for a sufficiently flammable solid, there are no other eigenvalues in the right half plane.

This is joint work with Anna Ghazaryan (University of North Carolina at Chapel Hill), Yuri Latushkin (University of Missouri), and Aparecido de Souza (Universidade Federal de Campina Grande).