Siegel

Albert-Ludwigs-Universität Freiburg
Mathematisches Institut
Abteilung für Reine Mathematik
Arbeitsgruppe Analysis

Introduction to Parabolic Partial Differential Equations im Sommersemester 2019/2020

Dozentin:   Dr. Azahara DelaTorre Pedraza (Sprechstunde: Di, 15-16 Uhr, Raum 214)
Assistent:   Dr. Lothar Schiemanowski (Sprechstunde: Di 9-11 Uhr, Do 9-11 Uhr, Raum 205)

Zeit:  Donnerstag, jeweils 12-14 Uhr
Ort:  Ernst-Zermelo-Str. 1, SR 404
 

Special dates in the Week June 3-7

The lecture on June 6 and the exercise class on June 7 have been moved to:
Lecture: June 3rd, 10-12, Room 218
Exercises: June 3rd, 12-14 Room 125

Syllabus

This course provides an introduction to the theory of parabolic partial differential equations.
Such equations arise in many applications, such as heat conduction and other physical and biological models. The following topics will cover the major part of the lecture.
1. The one- and multidimensional heat equation, fundamental solution, elementary methods and representation formulas.
2. Maximum principles for general linear parabolic equations.
3. Weak solutions and Galerkin-Method
4. If time permits, we will discuss some semi-group approaches.
5. We will keep having an eye on applications, such as random walks and models from finance.

The content is disjoint from the content of the course 'Partielle Dierentialgleichungen' by Prof. Wang and could well be attended complementary. The presentation will be at a basic level and technicalities are kept to a minimum.

Literature:
1.) Lawrence C. Evans, Partial dierential equations, AMS, Graduate studies in mathematics 19
2.) Sandro Salsa, Partial Differential Equations in Action, Springer Universitext, 2008.
3.) Walter Strauss, Partial Differential Equations, John Wiley & Sons, 1992.

Lecture notes

The file has been removed after the end of the lecture.

Exercises

Zeit:  Freitag, 8-10 Uhr
Ort:  Ernst-Zermelo-St. 1, SR 218
 
New exercise sheets will be uploaded every Friday. Solutions are to be handed in by Thursday, 12.00 the following week. Please put them in the mail box of Lothar Schiemanowski on the third floor.
Sheet Date
Sheet 1 May 2nd
Sheet 2 May 9th
Sheet 3 May 16th
Sheet 4 May 23th
Sheet 5 May 31st
Sheet 6 June 21st
Sheet 7 (see file)
Sheet 8 July 4th
Sheet 9 July 11th
Sheet 10 July 18th

Exam and credits

TBA