DG-MP-PDE Seminar: Traveling Fronts in Combustible Media

Traveling fronts are special solutions of reaction-diffusion equations which model phenomena such as propagation of species in an environment or spreading of flames in combustible media. In this talk we will address questions of existence, uniqueness, and stability of traveling fronts in general inhomogeneous media. We will show that in certain circumstances a unique front exists and it is a global attractor of the corresponding parabolic evolution, thus describing long time dynamics for very general solutions of the PDE. In contrast to this, we will also present examples of media where no traveling front solutions exist.