| Seminar information archive -05/16 | Future seminars 05/17- | Seminars | Graduate School of Mathematical Sciences | Access |
16:30 - 18:00Room #118 (Mathematics building)
Norbert Pozar (Graduate School of Mathematical Sciences, The University of Tokyo)
"Viscosity solutions for nonlinear elliptic-parabolic problems" (ENGLISH)
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]. This talk is based on a
recent work with Inwon Kim.