ISem23

Dear Participants of ISem 23,

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

https://www.mat.tuhh.de/veranstaltungen/isem23/_media/lecture_13.pdf

or in the forum.

The remaining two lectures of this internet seminar deal with continuity statements of the solution operator in the coefficients under various operator topologies. The first part will focus on ordinary differential equation.

The most important example will be equations of the form $\partial_{t,\nu} U_n + V_n(\mathrm{m})U_n=F$, where $(V_n)_n$ is a bounded sequence of bounded functions. The main theorem of the present lecture will characterise weak convergence of $(U_n)_n$ in terms of suitable convergence of $(V_n)_n$. This characterisation and the differential equation satisfied by the limit of $(U_n)_n$ might be surprising.

It is a great pleasure for us to use the forum interacting with the participants and to see that still many active readers follow the lecture note material. Also we very much appreciate the effort of the participants in solving the exercises and sending them to us.

For Lecture 13, we particularly ask the team from Dresden to submit `official' solutions for us to upload.

With the best regards,

the virtual lecturers