Title: Nonlinear stability of high Lewis number combustion fronts

Authors: Anna Ghazaryan

Issue: Volume 58 (2009), Issue 1, 181-212

Abstract: In this paper a mathematical model is considered that describes combustion processes characterized by a very high Lewis number. The model is known to support a wavefront that asymptotically connects the completely burned and the unburned states, and that is unique up to translation. The stability of the front has not yet been investigated beyond the spectral level. The essential spectrum of the linearization of the system about the front touches the imaginary axis, therefore, even in a parameter regime that guarantees absence of the unstable discrete spectrum, spectral information is not definitive. There exists an exponentially weighted norm that stabilizes the front on the linear level. The nonlinear stability in that exponentially weighted norm cannot be simply inferred from the spectral stability because the nonlinearity is not smooth in that norm. We use the interplay of the norms with and without exponential weight to overcome this issue, and show that the front in the co-moving frame is nonlinearly stable in the exponentially weighted norm with respect to a special class of perturbations.