Nonlinear elliptic-parabolic problems
Analysis of PDEs
2015-06-04 v1
Abstract
We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are proved via the comparison principle. In particular, we show existence and stability properties of maximal and minimal viscosity solutions for a general class of initial data. These results are new even in the linear case, where we also show that viscosity solutions coincide with the regular weak solutions introduced in [Alt&Luckhaus 1983].
Keywords
Cite
@article{arxiv.1203.2224,
title = {Nonlinear elliptic-parabolic problems},
author = {Inwon C. Kim and Norbert Pozar},
journal= {arXiv preprint arXiv:1203.2224},
year = {2015}
}
Comments
43 pages, 6 figures