Description:

Diese Veranstaltung baut auf dem Kursmaterial von Partielle Differentialgleichungen I im vorangegangenen Sommersemester auf. Methoden für lineare partielle Differentialgleichungen werden vertieft und erweitert auf nichtlineare partielle Differentialgleichungen. Behandelt wird u. A. die Theorie monotoner und maximal monotoner Operatoren. 

Language: English

Exam: The exam will be oral and will take place on March 6 and 7. Nachklausur: April 4.

Literature:
Chapter 1: Preliminaries.
- R. Adams, "Sobolev spaces".
- H. Brézis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations".
- L.C. Evans, "Partial Differential Equations".

Chapter 2: The Theory of Monotone Operators.
- E. Zeidler, "Nonlinear Functional Analysis and its Applications II/B".

Chapter 3: Maximal Monotone Operators.
- V. Barbu and T. Precupanu, "Convexity and Optimization in Banach spaces".
- E. Zeidler, "Nonlinear Functional Analysis and its Applications II/B".
- E. Zeidler, "Nonlinear Functional Analysis and its Applications III".

Chapter 4: Time-dependent Problems.
- L.C. Evans, "Partial Differential Equations".
- T. Roubíček, "Nonlinear Partial Differential Equations with Applications".

Lectures:

 - Tuesdays 08:15-09:45, A6/SR 007/008 Seminarraum (Arnimallee 6)
    Starting 15.10.2024
 - Thursdays 08:30-10:00, A6/SR 007/008 Seminarraum (Arnimallee 6)
    Starting 17.10.2024

Übung:

Tuesdays 16:15-17:45, A3/SR 120 (Arnimallee 3-5)
Starting 22.10.2024

The exercise sheets are to be solved in fixed teams of 2-3 persons and to be submitted electronically through Whiteboard as a pdf by the date specified on each exercise sheet. Their solutions will be presented by one of the students and further discussed in the exercise class.

Criteria to obtain the credit points for the course:
1. Regular participation in the exercise classes (attendance of at least 50% of the exercise classes - i.e. Tuesday afternoon lectures);
2. Active participation in the exercise classes is obtained by acquiring 50% of the total number of points for the exercises, and demonstration of one’s own solution at the blackboard in class.
3. Passing of the module exam.