Global Stability of Sharp Traveling Waves for Combustion Model with Degenerate Diffusion

This paper is concerned with the global nonlinear stability of sharp traveling waves for combustion model with degenerate diffusion. We prove that the solutions to the Cauchy problem converge to the unique sharp traveling wave (with a shift depending on the initial data), even the perturbation can be allowed arbitrarily large within the admissible range. Note that the traveling wave and the solution are at most Hölder continuous, and their supports are semi-compact. The degenerate diffusion and the low regularity make the study nontrivial. The proof is based on the monotonicity principle to which we add some new aspects.