Tuesday Seminar of Analysis

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.)
Organizer(s) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

2012/05/22

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Norbert Pozar (Graduate School of Mathematical Sciences, The University of Tokyo)
Viscosity solutions for nonlinear elliptic-parabolic problems (ENGLISH)
[ 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]. This talk is based on a
recent work with Inwon Kim.