Lecture notes on semigroup theory for linear evolution equations

Question

I am reading (or trying to read :)) "One parameter semigroups for Linear Evolution equations" by Klaus-Jochen Engel and Rainer Nagel. I was wondering if someone was aware of a good set of lecture notes for a course given at a university using this particular book or some such similar textbook. I feel that the information in the book is a bit overwhelming if one tries to read every single thing written on the book. (For now I am only interested in Chapters I through III). I want to be able to look at a set of lecture notes and concentrate on the most important topics one needs to know for an absolute beginner in the study of semigroups for evolution equations. If an expert can list some topics/theorems as absolute essentials then that would help as well. I hope this question is not too broad.

My specific interests are (applied) dynamical systems and spectral theory. I have a good background in real variables, functional analysis and complex analysis.

Thanks.

Answer 1

The lecture notes of the various Internet Seminars on Evolution Equations (http://www.math.kit.edu/iana3/page/isem/en) sound like something you'll enjoy. The topics vary with each seminar, but all are based on semigroup theory.

I participated in the 16th internet seminar, and I found the lecture notes from this seminar quite illuminating (particularly when paired with Engel-Nagel). The notes are at https://isem.math.kit.edu/index.php5/Phase_1:_The_lectures.

Enjoy!

Answer 2

Just to expand the answer by Alex, let me mention that the internet seminar of last year:

http://isem17.unisa.it/w/index.php/Phase_1:_The_lectures

was intended as a gentle introduction where a lot of time was spent on finite dimensional theory to motivate the ideas in a simpler situation. Though it stresses the positivity aspects of spectral theory, I am sure parts of it can also be used as a general introduction.