Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations
Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations
We study coarsening phenomena observed in discrete, ill-posed diffusion equations that arise in a variety of applications, including computer vision, population dynamics and granular flow.Our results provide rigorous upper bounds on the coarsening rate in any dimension.Heuristic arguments and the numerical experiments we perform indicate that the bounds are in …