A two-dimensional model for the upward propagating flame in a vertical square channel is explored. It is proved that under certain special initial conditions, the point where the flame interface attains its maximum, stays off the boundary (channel's wall) for an exponentially long period of time. The proof is an extension of the analysis developed previously for the one-dimensional version of the problem.
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Henry Berestycki, Shoshana Kamin, Gregory I. Sivashinsky, Leonid S. Kagan, Metastable behavior of premixed gas flames in rectangular channels. Interfaces Free Bound. 6 (2004), no. 4, pp. 423–438DOI 10.4171/IFB/108