Stability in a two-dimensional combustion model

Abstract

We study the stability of a planar travelling wave in the two-dimensional NEF-combustion model when the reduced Lewis number is equal to zero. The functional analytic setting consists of spaces of suitably exponentially weighted Hölder continuous functions. By exploiting the appearance of the integrated Burgers' equation in the equations for perturbations of the wave we avoid the usual assumption that the perturbation must be localized in the lateral space coordinate.