DIFFERENTIAL EQUATIONS IN BANACH SPACES — SS 2023/24
Office hours: write me an e-mail and we arrange a meeting...
Basic information
- Lecture on Tuesday from 9:00 in the room K11
- The exam is usually in the form of homeworks submitted during the semester.
- The following page is devoted to the first half of the semester. In the second half the lecturer will be D. Pražák.
- Basic literature: K.J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, 2000. (parts of chapters I a II)
Lecture
Content of the course can be found in [EN'2000], Sections I.5 (properties of semigroups), II.1 (generator and resolvent), II.6 (well-posedness),
II.3 (generation theorems) and the following:
Chapter 4 ... Self-adjoint semigroups on Hilbert spaces. presentation
Chapter 5 ... Analytic semigroups: Chapter5 (mp4), explanation (mp4), presentation (pdf)
Chapter 6 ... Asymptotic behaviour of semigroups: Chapter6-part1 (mp4), Chapter6-part2 (mp4), Chapter6-part3 (mp4), presentation (pdf)
.
Homeworks
You can submit the HW via e-mail or you can give it to me before the lecture.
HW1 ... multiplicative semigroups (till March 7).
HW2 ... shift semigroups and generation theorems (till March 28).
HW3 ... self-adjoint semigroups on Hilbert spaces (till April 4).
HW4 ... regularity of semigroups (till April 11).
Further reading
[EN] K.J. Engel, R. Nagel: One-parameter semigroups for linear evolution equations, Springer, 2000.
[Dav] E.B. Davies: Spectral theory and differential operators, Cambridge university press, 1995.
[SY] G.R. Sell, Y. You: Dynamics of evolutionary equations, Springer, 2002.