A contribution to the quarter-plane problem in diffraction theory

DOI10.1016/0022-247X(88)90396-4zbMath0696.35036OpenAlexW2001417417MaRDI QIDQ910557

Erhard Meister, Frank-Olme Speck

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(88)90396-4

zbMATH Keywords

Dirichlet problemHelmholtz equationNeumann problemquarter-plane problemWiener-Hopf operator theory

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Representations of solutions to partial differential equations (35C99)

Related Items (19)

Explicit solution of a Dirichlet-Neumann wedge diffraction problem with a strip ⋮ Some interior and exterior boundary-value problems for the Helmholtz equation in a quadrant ⋮ Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary ⋮ Bessel potential operators for the quarter-plane ⋮ Elastodynamical scattering by \(N\) parallel half-planes in \(\mathbb{R}^3\). II: Explicit solutions for \(N=2\) by explicit symbol factorization ⋮ Electromagnetic scattering by a plane angular sector. I: Diffraction coefficients of the spherical wave from the vertex ⋮ A class of interface problems for the Helmholtz equation in Rn ⋮ The discrete Dirichlet problem. Solvability and approximation properties ⋮ Unnamed Item ⋮ Double-knife edge problems with elastic/plastic type screens ⋮ Unnamed Item ⋮ Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions ⋮ Scattering of acoustic waves by a sector ⋮ A Robin boundary value problem in the upper half plane for the Bitsadze equation ⋮ Mixed boundary value problems of diffraction by a half‐plane with an obstacle perpendicular to the boundary ⋮ Wave diffraction by wedges having arbitrary aperture angle ⋮ Diffraction from a three-quarter-plane using an abstract Babinet principle ⋮ Diffraction from Polygonal-conical Screens, an Operator Approach ⋮ Diffraction by a rectangular wedge: Wiener-Hopf-Hankel formulation

Cites Work

• Diffraction by a quarter-plane
• Mixed boundary value problems of the type of Sommerfeld's half-plane problem
• Diffraction problems with impedance conditions
• General Wiener-Hopf Operators
• Toeplitz operators in a quarter-plane
• Integral equations on a half-line with kernel depending upon the difference of the arguments
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