Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Analysis-Seminar Augsburg-München

 

Professor Dr. Andre Schlichting
Universität Aachen

 
spricht am
 
Donnerstag, 14. Juni 2018
 
um
 
15:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»A non-local Fokker-Planck equation related to nucleation and coarsening«

Abstract:
In this talk we consider a Fokker-Planck equation modeling nucleation of clusters very similar to the classical Becker-Döring equation. The main feature of the equation is the dependence of the driving vector field and boundary condition on a non-local order parameter related to the excess mass of the system. In this way the equation has formally the structure of a McKean-Vlasov equation, but with a non-local boundary condition. We briefly discuss the well-posedness and regularity properties of the Cauchy-Problem. Here the main difficulty is to improve basic a priori regularity properties of the non-local 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



wwwadm@Math.Uni-Augsburg.DE,    Mi 23-Mai-2018 07:36:02 MESZ