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Einladung zum Mathematischen Kolloquium
Mittwoch, den 08.April 2026, 15:30 Uhr, Seminarraum A (R209),Institut für Mathematik
Abschiedskolloquium zu Ehren von Dr. Henning Behnke
Einladung zum Abschiedskolloquium zu Ehren von Dr. Henning Behnke
Mittwoch, den 08.April 2026, Seminarraum A (R209), Institut für Mathematik
Programm:
ab 15:00 Uhr gibt es für alle Interessierten die Möglichkeit zu einem Vorgespräch bei Kaffee und Tee im Sitzungszimmer (R110).
15:30 – 15:40 Uhr Prof. Dr. Andreas Potschka (geschäftsführender Leiter) Begrüßung und Verabschiedung
15:40 bis 16:45 Prof. Dr. Michael Plum Computer-assisted existence and multiplicity proofs for semi-linear elliptic boundary value problems
16:45 bis 16:50 Dr. Henning Behnke Abschiedsworte
Veranstalter: Institut für Mathematik, Erzstraße 1, 38678 Clausthal-Zellerfeld
Vortrag: Computer-assisted existence and multiplicity proofs for semi-linear elliptic boundary value problems
by Prof. Dr. Michael Plum
Abstract: Many boundary value problems for semi-linear elliptic partial differential equations allow very stable numerical computation of approximate solutions, but are still lacking analytical existence proofs. In the lecture, a method is proposed which exploits the knowledge of a „good“ numerical approximate solution in order to provide a rigorous proof of existence of an exact solution close to the approximate one. This goal is achieved by a Newton-Kantorovich-type fixed-point argument which takes all numerical errors into account, and thus gives a mathematical proof which is not „worse“ than any purely analytical one. A significant role in this fixed-point argument is played by eigenvalue bounds for the linearization of the given boundary value problem at the approximate solution. The method is used to prove existence and multiplicity statements for many specific examples of boundary value problems on bounded and on unbounded domains, with focus on cases where purely analytical methods had not been successful.
Link für die online Teilnahme am Kolloquium:
https://webconf.tu-clausthal.de/rooms/ola-qyv-ml6-ivd/join