BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Plum (Karlsruhe Institute of Technology) DTSTART:20200707T140000Z DTEND:20200707T150000Z DTSTAMP:20260423T023942Z UID:CRM-CAMP/3 DESCRIPTION:Title: Computer-assisted existence and multiplicity proofs for semilinear ellipt ic problems on bounded and unbounded domains\nby Michael Plum (Karlsru he Institute of Technology) as part of CRM CAMP (Computer-Assisted Mathema tical Proofs) in Nonlinear Analysis\n\n\nAbstract\nMany boundary value pro blems for semilinear elliptic partial differential equations allow very st able numerical computations of approximate solutions\, but are still lacki ng analytical existence proofs. In this lecture\, we propose a method whic h exploits the knowledge of a "good" numerical approximate solution\, in o rder to provide a rigorous proof of existence of an exact solution close t o the approximate one. This goal is achieved by a fixed-point argument whi ch takes all numerical errors into account\, and thus gives a mathematical proof which is not "worse" than any purely analytical one. A crucial part of the proof consists of the computation of eigenvalue bounds for the lin earization of the given problem at the approximate solution. The method is used to prove existence and multiplicity statements for some specific exa mples\, including cases where purely analytical methods had not been succe ssful.\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/3/ END:VEVENT END:VCALENDAR