ISem23

Dear Participants of ISem 23,

We have just uploaded the eleventh lecture, which you can find at the following link

https://www.mat.tuhh.de/veranstaltungen/isem23/_media/lecture_11.pdf

or in the forum.

The first lecture in the year 2020 is concerned with exponential stability of evolutionary equations. Since the focus of evolutionary equations is on inhomogeneous problems rather than initial value problems, we need to define what it means for an evolutionary equation to be exponentially stable.

As a rule of thumb, one can think of exponential stability as the possibility to extend the causal(!) solution operator defined for large enough $\nu>0$ to $L_{2,-\nu_0}(\mathbb{R};H)$ for some $\nu_0>0$. For this we again need some machinery from complex analysis.

We encourage everyone to be active in the forum as well as in solving the provided exercises. We particularly ask the team from Wuppertal to provide the official solutions for us to upload.

With the best regards,

the virtual lecturers