We study a diffraction of a plane wave incident to a periodic surface separating two dielectric materials with different real dielectric coefficients. Existence and uniqueness of solution to a periodic knitting problem for the Helmholtz equation is proved. Moreover we prove that the solution can be
Screen Problem for Vector Helmholtz Equation
โ Scribed by L. Sigua
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 473 KB
- Volume
- 206
- Category
- Article
- ISSN
- 0025-584X
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โฆ Synopsis
The paper deals with the screen boundary value problem for vector Helmholtz equation in the three-dimensional space. Using the method of boundary integral equations and the theory of elliptic pseudodifferential operators on manifolds with boundary we prove uniqueness and existence theorems in Bessel-potential and Besov spaces and establish Co -smoothness (with a < 1/2) of solutions up to the boundary.
1991 Mathematics Subject Classification. 35 J05, 35Q60.
๐ SIMILAR VOLUMES
The eigenvalue problem for the Laplace operator is numerical investigated using the boundary integral equation (BIE) formulation. Three methods of discretization are given and illustrated with numerical examples.
## Abstract In this paper we shall define an inverse problem for the Helmholtz equation with imaginary part of the wave number being positive. The Cauchy data are known on the boundary of the half plane, but it is not known where the half axis, lying vertically in the upper half plane, is situated.
Dedicated to Professor George C. Hsiao on the occasion of his 60th birthday