IJPAM: Volume 37, No. 3 (2007)
EIGENSTRUCTURE OF THE EQUILATERAL TRIANGLE
PART IV: THE ABSORBING BOUNDARY
PART IV: THE ABSORBING BOUNDARY
Brian J. M
Cartin
Department of Applied Mathematics
Kettering University
1700 West Third Avenue, Flint, MI 48504-4898, USA
e-mail: bmccarti@kettering.edu
Cartin
Department of Applied Mathematics
Kettering University
1700 West Third Avenue, Flint, MI 48504-4898, USA
e-mail: bmccarti@kettering.edu
Abstract.Lamé's formulas for the eigenvalues and
eigenfunctions of the Laplacian on an equilateral triangle under
Dirichlet and Neumann boundary conditions are herein extended to
the Robin problem with an absorbing boundary condition. They are
shown to form a complete orthogonal system. Various properties of
the spectrum and modal functions are explored.
Received: April 4, 2007
AMS Subject Classification: 35C05, 35J05, 35P10
Key Words and Phrases: equilateral triangle, Laplacian eigenvalues/eigenvectors, Robin problem, absorbing boundary condition
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 3
