Approximation of Semigroups - Part 2

Dear Participants,

welcome back. We hope you enjoyed the break and used the extra time to familiarise yourself with semigroups.

This week we continue the study of approximation methods, and turn our attention to the question whether an operator generates a semigroup or not. It is a widely used technique in the theory of PDEs to show well-posedness of complicated equations by some approximations. In this lecture we follow this strategy and finally arrive at the fundamental theorem of Chernoff. As a consequence, we obtain convergence of the implicit Euler scheme under the stability condition, a statement known under the name Hille-Yosida Theorem. For this purpose, the arguments from Lectures 3 and 4 need to be refined. See more at the link below.

We kindly ask the team of Karlsruhe to provide the official solutions.

Best wishes and good reading,
your virtual lecturers

Alexander
András
Bálint
Petra

ISEM15_Lecture5.pdf

A corrected version will be uploaded soon, until then see:

Discussion of Lecture 5.

Solutions and discussion of the exercises.