Refined upper bounds on the coarsening rate of discrete, ill-posed diffusion equations
Selim Esedoḡlu, Dejan Slepčev · Nonlinearity · 2008
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 numerical experiments we perform indicate that the bounds are in agreement with the actual rate of coarsening. 1.