Berestycki, H.; Kamin, S.; Sivashinsky, G. Metastability in a flame front evolution equation. (English) Zbl 0991.35097 Interfaces Free Bound. 3, No. 4, 361-392 (2001). Summary: 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. Cited in 22 Documents MSC: 35Q80 Applications of PDE in areas other than physics (MSC2000) 80A30 Chemical kinetics in thermodynamics and heat transfer Keywords:upward propagating flames; interfaces; Burgers type equation; parabolic equations; stationary solutions; hyperbolic equation; metastability PDFBibTeX XMLCite \textit{H. Berestycki} et al., Interfaces Free Bound. 3, No. 4, 361--392 (2001; Zbl 0991.35097) Full Text: DOI