Premium
Wave Scattering in a 2–D Exterior Domain with Cuts: The Neumann Problem
Author(s) -
Krutitskii P.A.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200008)80:8<535::aid-zamm535>3.0.co;2-1
Subject(s) - neumann boundary condition , domain (mathematical analysis) , mathematics , helmholtz equation , mathematical analysis , fredholm integral equation , integral equation , boundary value problem , boundary (topology) , cauchy boundary condition , scattering , cauchy problem , initial value problem , physics , optics
The Neumann problem in the exterior of several obstacles and double sided screens (cracks) is studied for a propagative Helmholtz equation in 2 dimensions. Previously the unique solvability of this problem has been obtained if obstacles are non‐resonance domains [9]. In the present paper the solvability of this problem is proved in the general case by the method of interior boundaries. In doing so additional boundaries are introduced inside obstacles. The Neumann problem is reduced to integral equations containing Cauchy kernels on screens and next to a uniquely solvable Fredholm equation of the second kind on the whole boundary.