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- Title
Neumann problem for the Helmholtz equation in the exterior of nonclosed surfaces and the case of its explicit solution.
- Authors
Krutitskii, P.
- Abstract
The article presents a study which examines the boundary value problems for the Helmholtz and Laplace equations in the exterior of smooth nonclosed surfaces and closed Lipschitz surfaces. The study used x as Cartesian coordinates and a boundary Lipschitz domain G with a boundary S to represent Lipschitz surface. It mentions that mathematical inequality was applied to a function to obtain equations on constant and bounded operator. It provides various equations to illustrate boundary value problems on the surfaces. Results show the usefulness of Helmholtz and Laplace equations in testing numerical methods.
- Subjects
NUMERICAL solutions to boundary value problems; HELMHOLTZ equation; LAPLACE'S equation; LIPSCHITZ spaces; MATHEMATICAL domains; MATHEMATICAL inequalities; MATHEMATICAL constants; NUMERICAL solutions to operator equations; ALGEBRAIC functions
- Publication
Doklady Mathematics, 2012, Vol 86, Issue 3, p805
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S106456241206021X