Nonlinear elliptic-parabolic problems

Details Nonlinear elliptic-parabolic problems Nonlinear elliptic-parabolic problems

2012-03-10

arxiv.org/abs/1203.2224v1

Mathematics

Analysis of PDEs

43 pages, 6 figures

Scientific paper

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].

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