Interface motion in ill-posed diffusion equations

27 November 2014
Michael Helmers
We consider a discrete nonlinear diffusion equation with bistable nonlinearity. The formal continuum limit of this problem is an
ill-posed PDE, thus any limit dynamics might feature measure-valued solutions, phases interfaces, and hysteretic interface motion.
Based on numerical simulations, we first discuss the phenomena that occur for different types of initial. Then we focus on the case of
interfaces with non-trivial dynamics and study the rigorous passage to the limit for a piecewise affine nonlinearity.
  • PDE CDT Lunchtime Seminar