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:
The following list contains the preliminary plan for the lecture:
- Modeling with Reaction-Diffusion Equations
- Existence and Uniqueness of Solutions
- Regularity and Large-time Behavior of Solutions
- Applications to Classical Reaction-Diffusion Systems
- 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.
- Kursverantwortliche/r: Michael Kniely
Semester: WiSe 2023/24