The course provides an introduction to the area of reaction-diffusion (RD) equations. Applications cover the modeling of chemical reactions in a diffusive environment as well as biological processes and population dynamics. A characteristic feature of RD equations (and, more generally, RD systems) is the interplay of "local" reaction processes and "non-local" diffusion effects. A key issue is the question, whether such systems admit solutions globally in time, or whether a so-called blow-up phenomenon arises. Depending on time and interest of the audience, we may also consider more advanced models with cross-diffusive interactions. Likewise, applications to semiconductor physics often include an additional interaction with charge and temperature.

The following list contains the preliminary plan for the lecture:

  1. Modeling with Reaction-Diffusion Equations
  2. Existence and Uniqueness of Solutions
  3. Regularity and Large-time Behavior of Solutions
  4. Applications to Classical Reaction-Diffusion Systems
  5. Generalized Reaction-Diffusion Models
The intended target audience are students in the master's program "Mathematics", but interested students from other programs are equally welcome. However, note that the contents of the bachelor modules
  • Functional Analysis (M17)
  • Partial Differential Equations (M18)
are taken for granted.

The lecture series will start on Thursday, October 19.

The lecture is planned to take place every Thursday from 11:00 (s.t.) until 12:45 at the Johann von Neumann-Haus - 1.012 Rudower Chaussee 25 (RUD25). (The slightly extended lecture hours allow for more flexibility during the term, e.g., if a class has to be cancelled for some reason. At the end, the given lecture classes should sum up to 24 hours.)

The first exercise class will be on Thursday, October 19. The first exercise sheet will be prepared and discussed directly in the class.

The exercise classes are planned to take place every other Thursday from 13:15 (s.t.) until 15:00 at the Johann von Neumann-Haus - 1.011 Rudower Chaussee 25 (RUD25). (As for the lecture, the exercise hours are slightly extended to facilitate the distribution of 12 hours of exercise classes until the end of the semester.)

To participate in the course, it is strongly recommended to enrol oneself in this moodle course. The necessary enrolment key will be communicated in the first lecture on October 19, 2023. Interested students are, nevertheless, very welcome to contact me at "michael.kniely@hu-berlin.de" and to ask for this key already in advance. 

Semester: WiSe 2023/24