Mixed boundary value problems of the type of Sommerfeld's half-plane problem

DOI10.1017/S0308210500019211zbMath0626.35020MaRDI QIDQ3029424

Frank-Olme Speck

Publication date: 1986

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

boundary integral equationconstant coefficientsfactorizationtransmission conditionHilbert space methodsWiener Hopf equationSommerfeld half plane problem

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) PDEs with low regular coefficients and/or low regular data (35R05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items

Rawlins' problem for half-plane diffraction: its generalized eigenfunctions with real wave numbers ⋮ 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 ⋮ A factorisation procedure for two by two matrix functions on the circle with two rationally independent entries ⋮ Spectral theory and L∞‐time decay estimates for Klein–Gordon equations on two half axes with transmission: The tunnel effect ⋮ Elastodynamical scattering by \(N\) parallel half-planes in \(\mathbb{R}^3\). II: Explicit solutions for \(N=2\) by explicit symbol factorization ⋮ Unnamed Item ⋮ A Sommerfeld-Type Diffraction Problem with Second-Order Boundary Conditions ⋮ Sommerfeld Half-plane Problems with Higher Order Boundary Conditions ⋮ A class of interface problems for the Helmholtz equation in Rn ⋮ Image normalization of Wiener-Hopf operators and boundary-transmission value problems for a junction of two half-planes ⋮ Continuum limit of discrete Sommerfeld problems on square lattice ⋮ A contribution to the quarter-plane problem in diffraction theory ⋮ Elastodynamical Scattering by N Parallel Half-Planes in IR3 ⋮ Diffraction by a Strip and by a Half-plane with Variable Face Impedances ⋮ A Sommerfeld‐Type Diffraction Problem with Second‐Order Boundary Conditions ⋮ Mixed impedance boundary value problems for the Laplace-Beltrami equation ⋮ Wave diffraction by a strip with first and second kind boundary conditions: the real wave number case ⋮ Double-knife edge problems with elastic/plastic type screens ⋮ Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions ⋮ The impedance boundary-value problem of diffraction by a strip ⋮ On the Reduction of Linear Systems Related to Boundary Value Problems ⋮ Unnamed Item ⋮ Sommerfeld Diffraction Problems with Oblique Derivatives ⋮ Wave diffraction by wedges having arbitrary aperture angle ⋮ From Sommerfeld Diffraction Problems to Operator Factorisation ⋮ On a class of Hankel operators: Fredholm properties and invertibility ⋮ Diffraction from Polygonal-conical Screens, an Operator Approach ⋮ Wiener-Hopf factorization through an intermediate space

Cites Work

• Unnamed Item
• Unnamed Item
• A direct boundary integral equation method for transmission problems
• Eine Methode zur Lösung mehrdimensionaler Kopplungsprobleme
• Diffraction problems with impedance conditions
• Mixed Boundary Value Problems for Lamé's System in Three Dimensions
• The Explicit Wiener-Hopf Factorisation of A Special Matrix
• The sommerfeld half‐plane problem revisited, II the factoring of a matrix of analytic functions