IJPAM: Volume 50, No. 1 (2009)

INTEGRAL EQUATION METHOD FOR THE SOLUTION
OF THE DIRICHLET PROBLEM IN A PERTURBED
THREE-DIMENSIONAL LAYER

Yury Shestopalov$^1$, Yury Smirnov$^2$
$^1$Department of Mathematics
Faculty of Technology and Science
Karlstad University, Karlstad, SE 65188, SWEDEN
e-mail: [email protected]
$^2$Department of Mathematics
Penza State University
40, Ul. Krasnaya, Penza, 440017, RUSSIA
e-mail: [email protected]


Abstract.A Dirichlet boundary value problem for the Laplace equation in a three-dimensional layer with a local perturbation of the boundary is solved by the method of boundary integral equation (IE). The unique solvability of the IE and its Fredholm property are proved. A Galerkin method of the IE numerical solution aimed at the use of parallel computations is developed and justified.

Received: May 18, 2008

AMS Subject Classification: 35J05, 31A25, 35Q72, 35S15, 45E99

Key Words and Phrases: perturbed layer, boundary integral equation, Galerkin method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 1