Wintersemester 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.

08.02.2017: I 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.

02.12.2016: Lecture 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. instead.

20.11.2016: Lecture 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).

11.11.2016: Lecture 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.

04.11.2016: Lecture 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).

28.10.2016: The 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.