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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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