Instabilities in a two-dimensional combustion model with free boundary

We prove instability of the planar travelling wave solution in a two-dimens ional free boundary problem modelling the propagation of near-equidiffusion al premixed flames in the whole plane. We reduce the problem to a fixed bou ndary fully nonlinear parabolic system. The spectrum of the linearized oper ator contains an interval [0, omega(c)], omega(c) > 0, so we cannot constru ct backward solutions. We use an argument about stability of dynamical syst ems in Banach spaces in order to prove pointwise instability of the moving front.