A weakly nonlinear parabolic equation pertinent to the flame front dynamics subject to the buoyancy effect, and to a statistical description of biological evolution is considered. In the context of combustion it is shown that the parabolic interface occurring in upward propagating flames in vertical channels may actually be merely quasi-equilibrium transient states which eventually collapse to a stable configuration in which the flame tip slides along the channel wall.
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Henry Berestycki, Shoshana Kamin, Gregory I. Sivashinsky, Metastability in a flame front evolution equation. Interfaces Free Bound. 3 (2001), no. 4, pp. 361–392DOI 10.4171/IFB/45