Prof. Dr. Robert Denk

  • Time and space: Tuesday, 16.00-16.45 in F 426, Thursday, 11.45-13.15, in F 426, first lecture on October 22nd, 2013.
  • There are no exercise groups for this lecture. The Tuesday class is dedicated to discussion and deepening of the knowledge. A list of possible topics and questions can be found here (Version of December 12th, 2013).
  • Language: english.

Contents
Literature
Lecture notes
Related Modules
Exam

Contents:

In this lecture series, we will consider parabolic differential equations as appearing, for instance, in models of heat conduction, fluid mechanics and phase transitions. In many applications the differential equation lives in a domain, and additional boundary conditions appear. For the analysis of nonlinear equation, maximal regularity is of central importance. In the lecture we will present parabolic boundary value problems and prove maximal regularity for them. One concept for the proof is the R-boundedness of operators.

Stochastic partial differential equations (SPDEs) appear in modelling of evolutionary systems if the data (e.g., the coefficients) depend on random perturbations. As an example, we mention turbulent flows which lead to stochastic Navier-Stokes equations. In this lecture series, we want to give a first insight into the concept and theory of SPDEs. Here we will use a mainly functional analytic approach. This leads to the interpretation of SPDEs as infinite-dimensional stochastic differential equations. This approach is similar to the semigroup approach for deterministic evolution systems. We will consider infinite-dimensional Wiener processes, stochastic integration in Hilbert spaces and maximal regularity for SPDEs.

For this lecture series, the student should have knowledge in functional analysis and on deterministic evolution equations. Basic knowledge of stochastics are required but not a deeper knowledge of  stochastic processes.

Literature:

Can be found at the end of the lecture notes.

Lecture notes:

The lecture notes (in German) will be updated regularly and can be found here.

Related Modules:

  • Masterstudiengang Mathematik (88105H)
      6000 Spezialisierungsmodule
        6100 Spezialisierungsmodule
  • Masterstudiengang Mathematik (88105H)
      3000 Wahlmodule
         3100 Wahlmodule 
  • Lehramtsstudiengänge WPO 2001
         (Staatsexamen)
           Mathematik
             Hauptstudium Vorlesungen 
  • Diplomstudiengänge
         Mathematik
             Hauptstudium Vorlesungen

Exam:

The module exam will take place in form of an oral exam which can be arranged individually.