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.
2010
spectral problem; trapped modes; localization of eigenfunctions
File in questo prodotto:
File Dimensione Formato  
CaDuNaSIAM.pdf

non disponibili

Licenza: Non specificato
Dimensione 433.17 kB
Formato Adobe PDF
433.17 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12070/6363
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 31
  • ???jsp.display-item.citation.isi??? 29
social impact