Stability in a two-dimensional free boundary combustion model

We prove rigorously the stability of the planar travelling wave solution to a free boundary system in R-2, arising as a model in combustion theory, for appropriate values of the reduced Lewis number. After changements of coordinates and unknowns, the problem is reduced to the stability of the null solution of a fixed boundary parabolic system. The difficulties consist in the fact that the final system is fully nonlinear, and the spectrum of the linearized system contains the halfline (-infinity,0]. They are overcome setting the problem in a suitably weighted Holder space. (C)2003 Elsevier Science Ltd. All rights reserved.