Two cases of squares evolving by anisotropic diffusion
Analysis of PDEs
2013-03-08 v1
Abstract
We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both equations. We construct explicit solutions showing the creation of facets, i.e. flat regions of solutions. By using the formula for solutions, we rigorously prove that both equations create ruled surfaces out of convex initial conditions as well as do not admit point (local) extrema. We present numerical experiments suggesting that the two flows seem not differ much. Possible applications to image reconstruction is pointed out, too.
Cite
@article{arxiv.1303.1655,
title = {Two cases of squares evolving by anisotropic diffusion},
author = {Piotr B. Mucha and Monika Muszkieta and Piotr Rybka},
journal= {arXiv preprint arXiv:1303.1655},
year = {2013}
}