Vorträge in der Woche 28.11.2016 bis 04.12.2016

Dienstag, 29.11.2016: Periods and the Eichler-Shimura isomorphism

Viktor Strehlau

Donnerstag, 01.12.2016: Spektrale Abbildungssätze

K. Király (Tübingen)

Wir betrachten Klassen von Halbgruppen, die verschiedene spektrale Abbildungssätze erfüllen. Mit Hilfe geeigneter Beispiele grenzen wir diese gegeneinander ab und können diese charakterisieren.

Donnerstag, 01.12.2016: On a class of nonlocal wave equations from applications

Prof. Horst Beyer

We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form a system of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain Rn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation