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SUMMARY:Random acoustic boundary conditions and Weyl's law [Oberseminar An
 alysis]
DTSTART:20251218T131500Z
DTEND:20251218T151500Z
DTSTAMP:20260308T042600Z
UID:indico-event-994@math-events.uni-bonn.de
DESCRIPTION:Speakers: Illia Karabash (Bonn University)\n\nMotivated by eng
 ineering and Photonics research on  resonators in random or uncertain env
 ironments\,we introduce rigorous randomizations of boundary conditions for
  acoustic wave equations in Lipschitz domains.First\, a parametrization of
  essentially all m-dissipative boundary conditions in the boundary L2-spac
 e is constructed with the use of boundary tuples.Randomizations of these b
 oundary conditions lead to acoustic operators random in the resolvent sens
 e.We prove this using Neumann-to-Dirichlet maps and generalized Krein reso
 lvent formulae.We give a description of  random m-dissipative boundary co
 nditionsthat produce acoustic operators with almost surely (a.s.) compact 
 resolvents\,and so\, also with a.s. discrete spectra.Based on these result
 s\, examples of mathematically convenient randomizations are constructedin
  terms of eigenfunctions of the Laplace-Beltrami operator on the boundary.
 We show that\, for these special randomizations\, the resolvent compactnes
 s is connectedwith the  Weyl law for the Laplace-Beltrami eigenvalues\, a
 nd also discuss availableWeyl-asymptotic results for the case of  nonsmoo
 th boundaries.\n\nhttps://math-events.uni-bonn.de/event/994/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/994/
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