On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:381

Article

de Oliveira, Cesar R.¹  Verri, Alessandra A.¹ 

[1] Univ Fed Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil

关键词: Spectrum;    Thin tubes;    Laplacian;    Dimensional reduction;   

DOI  :  10.1016/j.jmaa.2011.03.022

来源: Elsevier

【 摘 要 】

We study the Laplacian in deformed thin (bounded or unbounded) tubes in R(3), i.e., tubular regions along a curve r(s) whose cross sections are multiplied by an appropriate deformation function h(s) > 0. One of the main requirements on h(s) is that it has a single point of global maximum. We find the asymptotic behaviors of the eigenvalues and weakly effective operators as the diameters of the tubes tend to zero. It is shown that such behaviors are not influenced by some geometric features of the tube, such as curvature, torsion and twisting, and so a huge amount of different deformed tubes are asymptotically described by the same weakly effective operator. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free