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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.

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