ASYMPTOTIC BEHAVIOR OF A FRONT PROPAGATION MODEL: CASE OF A ONE-DIMENSIONAL FREE BOUNDARY PROBLEM

We consider a physical model of straight flame front propagation in a homogeneous solid medium in one space dimension governed by a free boundary problem. The position of the flame front at time is and is the temperature at time in the domain bounded by the front. We are particularly interested in the evolution over time of the pair . We define a notion of traveling wave solution or stationary wave solution, the couple with a front propagation velocity and a stationary temperature. We show that the solution of our problem converges to a wave solution when . Finally, the theoretical results are confirmed by various numerical tests.