The Helmholtz equation in the exterior of slits in a plane with different impedance boundary conditions on opposite sides of the slits

DOI10.1090/S0033-569X-08-01117-4zbMath1163.35342OpenAlexW1987093918MaRDI QIDQ3625436

P. A. Krutitskii

Publication date: 5 May 2009

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/distribution/qam/2009-67-01/S0033-569X-08-01117-4/home.html

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations with kernels of Cauchy type (45E05)

Related Items (12)

Quadrature formula for a double layer potential in the case of the Helmholtz equation ⋮ Problem for the Helmholtz equation in the exterior of nonclosed surfaces with an impedance boundary condition ⋮ Quadrature formula for the direct value of the double-layer potential ⋮ Improved quadrature formula for a single-layer potential ⋮ Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain ⋮ Explicit solution of the Helmholtz equation in the exterior of nonclosed Lipschitz surfaces with an impedance boundary condition ⋮ The direct scattering problem for a crack buried in a piecewise homogenous medium ⋮ Reconstruction of cracks of different types from far‐field measurements ⋮ The direct and inverse scattering problems for penetrable and impenetrable mixed obstacles ⋮ Mixed boundary value problems of diffraction by a half‐plane with an obstacle perpendicular to the boundary ⋮ Mixed type boundary value problems for Laplace-Beltrami equation on a surface with the Lipschitz boundary ⋮ Boundary integral method for scattering problems with cracks buried in a piecewise homogeneous medium

Cites Work

• A generalization of the Neumann problem for the Helmholtz equation outside cuts on the plane
• DEVELOPMENT OF THE DIRECT BOUNDARY ELEMENT METHOD FOR THIN BODIES WITH GENERAL BOUNDARY CONDITIONS
• An explicit solution of the pseudo‐hyperbolic initial boundary value problem in a multiply connected region
• An Existence Theorem for the Reduced Wave Equation
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