Prof. Dr. Robert Denk
- Time and place: Mo 10-12 in F 426
- Lecture notes in German
Content: In this lecture we will apply the theory of semigroups (theory of evolution equations) to partial differential equations. We will focus on parabolic differential equations which are used to model, e.g., heat conduction, fluid mechanics and phase transitions. Another application is the value of a stock option.
Semigroup theory allows us to treat partial differential equations in an abstract and unified way. With this approach, one can obtain results on unique solvability and estimates on the solution. In many applications the differential equations live in a domain instead of the whole space. In this case one has to deal with boundary conditions.
This lecture is a continuation of a lecture on evolution equations (for instance, the lecture from summer semester 2008). The lecture on partial differential equations I is not required. In combination with the lecture on evolution equations or any other lecture in the field of partial differential equations, this lecture can be used for the exam in Hauptdiplom. Moreover, this lecture leads to a main seminar and/or diploma thesis in this area.
The lecture is adapted for students in the 6th semester or higher.
Literature will be announced in the lecture.