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PRODID:-//Memento EPFL//
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SUMMARY:Spectral analysis of a Neumann biharmonic operator on a dumbbell d
 omain
DTSTART:20161207T150000
DTEND:20161207T161500
DTSTAMP:20260930T195009Z
UID:8307a993c9b9ff6d495170737242c54eaa5e0333132a072a558cb35c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Francesco Ferraresso (Università degli Studi di Padova)\nWe d
 iscuss the spectral behavior of the biharmonic operator subject to  bound
 ary conditions of Neumann type on a planar dumbbell domain\, in the spirit
  of the results obtained by J.M Arrieta and collaborators for the Neumann 
 Laplacian. By dumbbell domain we mean the union of two fixed bounded disjo
 int domains and a thin channel connecting the two components. The thicknes
 s of the channel depends on a small parameter and vanishes as such paramet
 er tends to zero. Thus\, in the limit the channel collapses to a segment. 
 We provide a full description of the limiting problem and of its spectrum.
  In particular\, we show that the eigenvalues of the dumbbell problem are 
 of two types: either they converge to an eigenvalue corresponding to the N
 eumann biharmonic operator in the fixed part of the dumbbell\, or they con
 verge to an eigenvalue corresponding to an ordinary differential equation 
 in the segment. Such ODE has a peculiar differential structure\, generally
  different from the original PDE. Finally\, we present some results concer
 ning the convergence of the eigenfunctions.\n\nThe talk is based on a join
 t work with J.M. Arrieta and P.D. Lamberti.
LOCATION:MA 10
STATUS:CONFIRMED
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