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By studying classical and recent literature, the students will gain a solid understanding of important aspects of the theory of strongly continuous operator semigroups and the application to linear and non-linear evolution problems

Since the middle of the past century, one-parameter semigroups of bounded linear operators play a prominent role in the analysis of partial differential equations, ranging over wide fields of applications. The aim of this seminar is to gain a solid understanding of important aspects of this theory. Starting from scratch, we will discuss selected topics including Generation Theorems, spectral theory for differential operators and Spectral Mapping, as well as the application of the theory to linear and non-linear evolution problems. The seminar will consist of presentations by the participants, based on classical and recent literature.

Presentations by participants based on classical and recent literature.

Active participation and evaluation of the presentation.

• K.-J. Engel and R. Nagel, A Short Course on Operator Semigroups, Springer 2006.
• T. Cazenave, A. Haraux, Y. Martel, An Introduction to Semilinear Evolution Equations, Oxford University Press 1999.
• A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.

Functional analysis, Basic course on Partial Differential Equations