Stochastic partial differential equations

Head:
Benjamin Gess (Email, Homepage)

Phone:
+49 (0) 341 - 9959 - 954

Fax:
+49 (0) 341 - 9959 - 658

Address:
Inselstr. 22
04103 Leipzig

Summerterm 2017

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.

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28.09.2021, 13:34