Where best to hold a drum fast

被引：11

作者：

Cox, SJ

Uhlig, PX

机构：

[1] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA

[2] St Marys Univ, Dept Math, San Antonio, TX 78228 USA

来源：

SIAM JOURNAL ON OPTIMIZATION | 1999年 / 9卷 / 04期

关键词：

membrane; eigenvalue; Robin; mixed; optimal design;

D O I：

10.1137/S1052623497326083

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If we are allowed to fasten, say, one half of a drum's boundary, which half produces the lowest or highest bass note? The answer is a natural limit of solutions to a family of extremal Robin problems for the least eigenvalue of the Laplacian. We produce explicit extremizers when the drum is a disk while for general shapes we establish existence and necessary conditions, and we build and test a pair of numerical methods.

引用

页码：948 / 964

页数：17

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