Some remarks on a viscous regularization of the nonlinear diffusion equation
Mathematical Physics
2015-06-01 v1 Analysis of PDEs
math.MP
Abstract
We illustrate an alternative derivation of the viscous regularization of the diffusion equation which was studied in [A. Novick-Cohen and R. L. Pego. {\em Trans. Amer. Math. Soc.}, 324:331--351]. We provide an alternative proof of existence of solutions, based on the Galerkin method and on compactness arguments. In addition, we propose a "non-smooth" variant of the viscous regularization which we believe may result in interesting hysteretic effects.
Keywords
Cite
@article{arxiv.1505.07993,
title = {Some remarks on a viscous regularization of the nonlinear diffusion equation},
author = {Giuseppe Tomassetti},
journal= {arXiv preprint arXiv:1505.07993},
year = {2015}
}