The variational approach to stochastic PDE

In this course we will consider the variational approach to stochastic partial differential equations with monotone drift, going back to N. V. Krylov, B. L. Rozovskii and E. Pardoux. A main benefit of this approach is that it allows to deal with degenerate quasilinear equations such as the (stochastic) porous medium equation $$du = \Delta (|u|^m u) dt + B(u_t)dW_t$$ and the (stochastic) p-Laplace equation $$du = \textrm{div} (|\nabla u|^p \nabla u) dt + B(u_t)dW_t.$$ After having established the well-posedness of solutions to this class of equations we will investigate qualitative questions on the long-time behavior, ergodicity and random dynamics.

Date and time info
Wednesday, 11:00 - 12:30

Keywords
Stochastic Partial Differential Equations, Stochastic Analysis

Prerequisites
basic measure theory, functional analysis, probability theory

Audience
MSc students, PhD students, Postdocs

Language
English