Universität Augsburg

Professor Dr. Andre Schlichting
Universität Aachen
spricht am
Donnerstag, 14. Juni 2018
um
15:00 Uhr
im
Raum 2004 (L1)
über das Thema:
Abstract: 
In this talk we consider a FokkerPlanck equation modeling nucleation of clusters very similar to the classical BeckerDöring equation. The main feature of the equation is the dependence of the driving vector field and boundary condition on a nonlocal order parameter related to the excess mass of the system. In this way the equation has formally the structure of a McKeanVlasov equation, but with a nonlocal boundary condition. We briefly discuss the wellposedness and regularity properties of the CauchyProblem. Here the main difficulty is to improve basic a priori regularity properties of the nonlocal order parameter. The main part of the talk focuses on the longtime behavior of the system. The system posses a free energy, which strictly decreases along the evolution and leads to a gradient structure involving boundary conditions. We generalize the standard entropy method based on suitable weighted logarithmic Sobolev inequalities and interpolation estimates. In this way, we obtain an explicit characterization of the convergence to equilibrium with algebraic or even exponential rates depending on the particular assumptions on the vector fields, diffusivity and initial data. (joint work with J. Conlon) 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Bernd Schmidt 