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Instabilities in a two-dimensional combustion model with free boundary. (English) Zbl 0984.76030
Summary: We prove instability of planar travelling wave solution in a two-dimensional free boundary problem modelling the propagation of near-equidiffusional premixed flames in the whole plane. We reduce the problem to a fixed-boundary fully nonlinear parabolic system. The spectrum of the linearized operator contains an interval $$[0,\omega_c]$$, $$\omega_c> 0$$, so we cannot construct backward solutions. Thus we use an argument about stability of dynamical systems in Banach spaces in order to prove the pointwise instability of moving front.

##### MSC:
 76E99 Hydrodynamic stability 76V05 Reaction effects in flows 80A25 Combustion 35B35 Stability in context of PDEs
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