Crack impedance-Dirichlet boundary value problems of diffraction in a half-plane
Keywords:
Crack, Helmholtz equation, wave diffraction, boundary value problem, potential method, Fredholm theory, oscillating symbol.
Abstract
We study two wave diffraction problems modeled by the Helmholtz equation in a half-plane with a crack characterized by Dirichlet and impedance boundary conditions. The existence and uniqueness of solutions is proved by an appropriate combination of general operator theory, Fredholm theory, potential theory and boundary integral equation methods. This combination of methods leads also to integral representations of solutions. Moreover, in Sobolev spaces, a range of smoothness parameters is obtained in which the solutions of the problems are valid.
Published
2015-08-28
Issue
Section
Articles