Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Analysis-Seminar Augsburg-München

 

Dr. Jonas Tölle
Universität Augsburg

 
spricht am
 
Donnerstag, 11. Januar 2018
 
um
 
15:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Stability of solutions and ergodicity for stochastic local and nonlocal p-Laplace equations«

Abstract:
We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider stochastic partial differential equations with drift given as the subdifferential of a convex function and prove continuous dependence of the solutions with regard to random Mosco convergence of the convex potentials. To this aim, we identify the concept of stochastic variational inequalities (SVI) as a well-suited framework to study such stability properties. In particular, we provide an SVI treatment for stochastic nonlocal p-Laplace equations and prove their convergence to the respective local models. Furthermore, ergodicity for local and nonlocal stochastic singular p-Laplace equations is proven, without restriction on the spatial dimension and for all p ∈ [1, 2). This generalizes previous results from [Gess, Tölle; J. Math. Pures Appl. (2014)], [Liu, Tölle; Electr. Comm. Probab. (2011)], [Liu; J. Evol. Equations (2009)]. In particular, the results include the multivalued case of the stochastic (nonlocal) total variation flow. Under appropriate rescaling, the convergence of the unique invariant measure for the nonlocal stochastic p-Laplace equation to the unique invariant measure of the local stochastic p-Laplace equation is proven.
The talk is based on joint work with Benjamin Gess (MPI Leipzig / Bielefeld University): [Gess, Tölle; J. Differential Equations (2016)], [Gess, Tölle; SIAM J. Math. Anal. (2016)].

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Lisa Beck



[Impressum]      [Datenschutz]      wwwadm@math.uni-augsburg.de,    Mi 10-Jan-2018 13:12:48 MESZ