NONLINEAR DYNAMICS AND METASTABILITY IN A BURGERS TYPE EQUATION (FOR UPWARD PROPAGATING FLAMES)

This Note concerns a nonlinear parabolic equation describing flame fro nt evolution in upward propagating flames subject to gravity in vertic al channels. The results we present here show that the parabolic front s - which are observed in experiments and in computations - may actual ly be merely quasi-equilibrium transient states. After an exponentiall y long time, these parabolic fronts indeed eventually collapse into a stable configuration in which the inclined front as it were spreads al ong the wall of the channel. The model, proposed in [10], reduces to t he following evolution problem: [GRAPHICS] In this Note we give a comp lete description of the stationary solutions, analyze their stability properties and discuss the dynamics of this problem for small epsilon.