Pinning of interfaces in random media
Patrick Dondl, Bonn University
We consider the evolution of an interface, modeled by a parabolic
equation, in a random environment. The randomness is given by a
distribution of smooth obstacles of random strength. To provide a
barrier for the moving interface, we construct a positive, steady state
supersolution. This construction depends on the existence, after
rescaling, of a Lipschitz hypersurface separating the domain into a top
and a bottom part, consisting of boxes that contain at least one
obstacle of sufficient strength. We prove this percolation result.
Joint work with N. Dirr (Bath University) and M. Scheutzow (TU Berlin).