1. Asymptotic behaviour of eigenfunctions in a thin cylinder with distorted ends
- Author
-
Tiziana Durante
- Subjects
localization of eigenfunctions ,Dirichlet conditions ,Mathematical analysis ,Zero (complex analysis) ,Geometry ,spectral problem, trapped modes, localization of eigenfunctions ,Mathematics::Spectral Theory ,Eigenfunction ,Lateral side ,spectral problem ,trapped modes ,symbols.namesake ,symbols ,Cylinder ,Boundary value problem ,Laplace operator ,Mathematics - Abstract
We consider a mixed boundary value problem for the Laplace operator in a straight cylinder with curved ends with the Dirichlet conditions on the lateral side. We prove that when the ratio between the diameter and the length of the cylinder tends to zero, the principal eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior.
- Published
- 2013
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