PDE Real Analysis Seminar

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Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2014/06/24

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Piotr Rybka (University of Warsaw)
Sudden directional diffusion: counting and watching facets (ENGLISH)
[ Abstract ]
We study two examples of singular parabolic equations such that the diffusion is so strong that is leads to creation of facets. By facets we mean flat parts of the graphs of solutions with singular slopes. In one of the equations we study there are two singular slopes. The other equation has just one singular slope and the isotropic diffusion term. For both problems we watch and count facet.

For the system with two singular slopes a natural question arises if any solution may have an infinite number of oscillations. We also show that the solutions we constructed are viscosity solutions. This in turn gives estimates on the extinction time based on the comparison principle.