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X-ORIGINAL-URL:https://dcn.nat.fau.eu/
X-WR-CALNAME:FAU DCN-AvH Chair for Dynamics, Control and Numerics -Alexander von Humboldt Professorship
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BEGIN:VEVENT
CLASS:PUBLIC
DTSTART;TZID=Europe/Berlin:20201014T080000
DTEND;TZID=Europe/Berlin:20201014T180000
DTSTAMP:20211020T062700
UID:MEC-76cac4685e3749728f9c04bd3a86221f@dcn.nat.fau.eu
CREATED:20211020
LAST-MODIFIED:20220117
PRIORITY:5
TRANSP:OPAQUE
SUMMARY:Analytic Properties of Heat Equation Solutions and Reachable Sets
DESCRIPTION:Organized by: FAU DCN-AvH, Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)\nSpeaker: Prof. Dr. Alden Waters\nAffiliation: University of Groningen (The Netherlands)\nZoom link\nMeeting ID: 916 1218 3377 | PIN code: 386119\nAbstract. We consider heat equations on bounded Lipschitz domains Omega in R^d and show that solutions to the heat equation for positive times are analytically extendable to a subdomain of the complex plane containing Omega. Our analysis is based on the boundary layer potential method for the heat equation. In particular, our method gives an explanation for the shapes appearing in the literature in 1d, which is not so easy to explain using Fourier analysis alone. I will also discuss the converse theorem, namely that certain sets in the complex plane can be realized as solutions to the heat equation on the boundary of Omega when Omega is a ball. Boundary layer potential theory also gives an indication that this statement is more difficult if Omega is not a ball. This exciting new technique to analyze the question of reachable sets is joint work with Alexander Strohmaier.\n
URL:https://dcn.nat.fau.eu/events/analytic-properties-of-heat-equation-solutions-and-reachable-sets/
CATEGORIES:FAU CAA Seminar,Seminar/Talk
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