The variational approach to stochastic PDE

  • Lecturer: Benjamin Gess
  • Date: Wednesday, 11:00 - 12:30
  • Room: MPI MiS, A3 01
  • Language: English
  • Target audience: MSc students, PhD students, Postdocs
  • Keywords: Stochastic Partial Differential Equations, Stochastic Analysis
  • Prerequisites: basic measure theory, functional analysis, probability theory
  • First class: May, 3rd, 2017

Abstract:

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.

Access Information

Please use the entry doors Kreuzstr. 7a (rooms A3 01, A3 02) and Kreustr. 7c (rooms G3 10, G2 01), both in the inner court yard, and go to the 3rd. floor (see the map). To reach the Leibniz-Saal use the main entry Inselstr. 22 and go to the 1st. floor.
Please note: The doors will be opened 15 minutes before the lecture starts and closed after beginning of the lecture!


Regular Lectures (Summer 2017)

05.07.2017, 15:48