2016/2017: Interactions between Dynamics and PDE
For all details regarding the course, please refer to the syllabus / course outline (may be updated at some point, please also compare news below).
IMPORTANT INFORMATION 1: Current lecture notes (updated regularly!)
IMPORTANT INFORMATION 2: It has been determined that there will be an oral exam at the end of the course!
IMPORTANT INFORMATION 3: The
last class 10.02. at 14:15 will be an open question session. I am also
going to provide some guidelines for studying for the exam.
10.02.2017: Lecture notes updated. It
has been decided that the last chapter covered today on the existence
of non-trivial stationary solutions for the cubic nonlinear wave
equation is not part of the exam. Hence, the last included section is
the one on mean-field limits, Section 17.
have added solutions for the last three exercises from the last
exercise class. The exercise on 'point dissipative' implies 'bounded
dissipative' in finite-dimensional spaces was done in the class, and
the presented geometric ideas were correct. However, some of you asked
if they could see a fully written out proof with all the details. I
have now done so in the notes and explained this exercise as detailed
as possible as an illustration.
03.02.2017: Lecture notes updated.
31.01.2017: I have added solutions and remarks for Exercises 10.15 and 10.16 as promised in the exercise class.
27.01.2017: Lecture notes updated. For
the next exercise class please try to do any four exercises out of:
13.13, 13.15, 14.8, 14.9, and 15.6. During the next few days I am also
going to add solutions for the last exercise class for two exercises
regarding exponential dichotomies.
20.01.2017: Lecture notes updated.
13.01.2017: Lecture notes updated. For
the next exercise class please try to any four exercises out of: 10.15,
10.16, 11.3, 12.6, and 12.7. Of course, you are encouraged to try all
five for practicing the material.
18.12.2016: As promised, I have worked out solutions to exercises 9.9 and 9.10 and put them into the notes.
16.12.2016: Lecture notes updated. Happy Christmas and Happy New Year. See you again on Friday 13.01.2017.
09.12.2016: Lecture notes updated. For
the next exercise class please try to do: 8.8, 8.10, 9.9, 9.10. Note
that we have agreed to move the class from 23.12. to 16.12. so that we
are going to have an additional lecture on 16.12. at 16:00 in the usual
room. In this lecture I am going to present topics
that we could cover in the last roughly two weeks of the course. There
will be a vote to determine, which topics you prefer.
notes updated; I have also added a solution to the
separation-of-variables exercise now after the class this afternoon.
Please note: I plan to show some numerical results for
the theoretical bifurcation problems we did so far in the second
lecture next week. There we shall see, how to find bifurcation diagrams
using numerical continuation techniques.
25.11.2016: Lecture notes updated. For
the next exercise class please try to do: 6.9, 6.10, 7.6, 7.7. If you
like numerics and want to see some of the analytical results on a
computer, you may substitute one of the four exercises by doing 7.8.
notes updated. I have now also provided an appendix in the lecture
notes with solutions to two exercises. As requested, the log-Sobolev
exercise 3.11. is now solved and I also wrote out a proof of the
maximum principle in the 1D case (exercise 3.10), as it seems a little
more cumbersome to write out than I thought it would be (feel free to
try to find an easier proof).
notes updated. For the next exercise class please try to do: 4.8, 4.9,
5.9., 5.10(a). If you would like to challenge yourself more, try
5.10(b) and the optional part in 5.10; I am happy to discuss these
parts of the exercise as well if someone has attempted them.
notes updated. We have decided to move the class from 23.12.2016 (i.e.
the day before Christmas) to the week before, i.e., we attach one
lecture after the second slot (say 16:00 to about 17:15 or 17:30).
schedule remains as proposed below, i.e., no changes, exercises will be
every other week on Friday afternoon. The updated lecture notes have
been posted. For the exercises next Friday, please try to do: 2.11, 2.12, 2.13, 3.8,
3.9, 3.10 (see lecture notes). See you next Friday.
21.10.2016: If you are interested in the course you can still start easily at the next lecture Friday Oct. 28th at 10:15! Also, scheduling is flexible and we may move things around if it is convenient for all the participants for later lectures (please watch this space!).
21.10.2016: Notes for the first lecture have been posted. Current plan for the next few lectures: Lecture 2: Friday Oct. 28th at 10:15 (2 x 45 minutes), Lecture 3: Friday Oct. 28th at 14:15 (2 x 45 minutes), Lecture 4: Friday Nov. 4th at 10:15 (2 x 45 minutes), Exercise Class 1: Nov. 4th at 14:15 (2 x 45 minutes)
For an old version of the lecture notes, click here.