A simple sufficient condition on a curved end of a straight cylinder is found that provides a localization of the principal eigenfunction of the mixed boundary value for the Laplace operator with the Dirichlet conditions on the lateral side. Namely, when the small parameter, i.e., the ratio between the diameter and the length of the cylinder, tends to zero, the eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior. Similar effects are observed in the Dirichlet and Neumann problems, too.
LOCALIZATION EFFECT FOR EIGENFUNCTIONS OF THE MIXED BOUNDARY VALUE PROBLEM IN A THIN CYLINDER WITH DISTORTED ENDS
Cardone G;
2010-01-01
Abstract
A simple sufficient condition on a curved end of a straight cylinder is found that provides a localization of the principal eigenfunction of the mixed boundary value for the Laplace operator with the Dirichlet conditions on the lateral side. Namely, when the small parameter, i.e., the ratio between the diameter and the length of the cylinder, tends to zero, the eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior. Similar effects are observed in the Dirichlet and Neumann problems, too.File in questo prodotto:
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