Abstract
We prove rigorously the stability of the planar travelling wave solution to a free boundary system in R2, 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 halffine (-∞, 0]. They are overcome setting the problem in a suitably weighted Holder space.
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