ISem23

Dear Participants of ISem 23,

We have just uploaded the fourteenth (and last) lecture of this academic year's internet seminar, which you can find at the following link

https://www.mat.tuhh.de/veranstaltungen/isem23/_media/lecture_14.pdf

or in the forum.

In the last lecture, we turn to address continuous dependence on the coefficients for evolutionary equations with $A\neq 0$. The theory for this case is somewhat complementary to what we have seen for the case of $A=0$. In order to treat problems that are different in nature from the ones discussed in Lecture 13, we need to ask for $A$ to be `really' unbounded.

The assumption for this is that $A$ should have compact resolvent, which in the case of infinite-dimensional Hilbert space asks for $A$ to be unbounded.

We will have occasion to discuss an equation of highly oscillatory mixed type. Furthermore, we will consider an application to homogenisation problems for the wave equation. This application is a bit more involved. Thus, in the last lecture, we slightly exceed our page limit. We genuinely hope that this exception is nonetheless a pleasure for everybody.

For the official solutions of the last lecture, we ask the team from Hamburg to prepare solutions for us to upload.

We want to express our great thank you to all the participants for having actively worked with the lecture notes material in Phase 1 of the internet seminar. It was and still is great to talk and engage with you about evolutionary equations.

We shall take a break and will soon let you know about Phase 2 and organisational matters regarding this.

For now, we are looking forward to Phase 2 of the internet seminar and eventually to seeing many of you personally in Phase 3 in Wuppertal this (European) summer.

With the best regards,

the virtual lecturers