Some recent investigations on interfacial propagation in inhomogeneous medium
Seminar Room 1, Newton Institute
We will present some results for the interfacial propagation in inhomogeneous medium. The prototype equation is given by motion by mean curvature. The key feature is the interaction between the mean curvature of the interface and the underlying spatial inhomogeneity. We will describe the transition between the pinning and de-pinning of the interface and the existence of pulsating waves. Some recent investigations on the pinning threshold, front propagations between patterns and random walks in random medium will also be discussed.