Abstract:
We prove instability of the 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,ωc], ωc > 0, so we cannot construct backward solutions. We use an argument about stability of dynamical systems in Banach spaces in order to prove pointwise instability of the moving front.
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(Accepted: January 31, 2000)¶Published online August 21, 2000
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Brauner, CM., Lunardi, A. Instabilities in a Two-Dimensional Combustion Model with Free Boundary. Arch. Rational Mech. Anal. 154, 157–182 (2000). https://doi.org/10.1007/s002050000099
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DOI: https://doi.org/10.1007/s002050000099