Universität Augsburg
|
Dr. Jonas Tölle
Universität Augsburg
spricht am
Donnerstag, 11. Januar 2018
um
15:00 Uhr
im
Raum 2004 (L1)
über das Thema:
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 |