Universität Wien

250308 VO Selected topics in partial differential equations (2007S)

Selected topics in partial differential equations

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 06.03. 15:00 - 16:30 Seminarraum
  • Tuesday 13.03. 15:00 - 16:30 Seminarraum
  • Tuesday 20.03. 15:00 - 16:30 Seminarraum
  • Tuesday 27.03. 15:00 - 16:30 Seminarraum
  • Tuesday 17.04. 15:00 - 16:30 Seminarraum
  • Tuesday 24.04. 15:00 - 16:30 Seminarraum
  • Tuesday 08.05. 15:00 - 16:30 Seminarraum
  • Tuesday 15.05. 15:00 - 16:30 Seminarraum
  • Tuesday 22.05. 15:00 - 16:30 Seminarraum
  • Tuesday 05.06. 15:00 - 16:30 Seminarraum
  • Tuesday 12.06. 15:00 - 16:30 Seminarraum
  • Tuesday 19.06. 15:00 - 16:30 Seminarraum
  • Tuesday 26.06. 15:00 - 16:30 Seminarraum

Information

Aims, contents and method of the course

1) Modelling:

* basics in continuum mechanics: Description of species/populations
as densities, Modelling of diffusion and reaction terms
* examples of prominent applications in chemistry, biology, physics, neurology, ...

2) Existence of solutions:

* local in time existence, regularity and uniquness of solutions, wellposedness
* global in time solutions: a-priori-estimates, diffusion induced instability
* miscroscopic viewpoint: RD systems a macroscopic limit of kinetic
equations, entropy methods
* extended solutions: weak solutions, renormalized solutions

3) Qualitative behaviour of seclected applications:

* systems with oscillations: Belousov and the Second Law of
Thermodynamics?
* extended Volterra-Lotka systems: competition and segregation
* pattern fromation: shells and music
*

Assessment and permitted materials

Minimum requirements and assessment criteria

We present Reaction-Diffusion equations as utterly important models in surprisingly many and various applications. After discussing the basic theory of existence, the focus lies in understanding the qualitative behaviour of selected examples providing an outlook to the rich behaviour of reaction-diffusion equations.

Examination topics

A lecure with features to stimulate discussions

Reading list

Paul C. Fife, "Mathematical Aspects of Reacting and Diffusing Systems" Lecture Notes in Biomathematics 28, Springer (1979) Franz Rothe, "Global Solutions of Reaction-Diffusion Systems" Lecture Notes in Mathematics 1072, Springer (1984)
James D. Murray, "Mathematical Biology" Springer (2002)

Association in the course directory

Last modified: Mo 07.09.2020 15:40