Journal ArticleDOI
Electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate
Simon N. Chandler-Wilde,Bo Zhang +1 more
TLDR
In this paper, the authors considered a two-dimensional problem of scattering of a time harmonic electromagnetic plane wave by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate.Abstract:
We consider a two-dimensional problem of scattering of a time harmonic electromagnetic plane wave by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate. The magnetic permeability is assumed to be a fixed positive constant in the media. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and a positive constant above the layer corresponding to a homogeneous dielectric medium. In this paper, we only examine the TM (transverse magnetic) polarization case. A radiation condition is introduced and equivalence with a second kind, Lippmann-Schwinger-type integral equation is shown. With additional assumptions on the index of refraction in the layer, uniqueness of solution is proved. Existence of solution is then established by employing a form of Fredholm alternative using a general result on the solvability of integral equations on unbounded domains published earlier by Chandler-Wilde and Zhang. An approximate analytic solution for the case of a thin inhomogeneous layer is obtained from the integral equation formulation and is used to show that, if the index of refraction is appropriately chosen, the scattered field can grow with distance from the plate.read more
Citations
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Journal ArticleDOI
Initial Boundary Value Problems in Mathematical Physics
TL;DR: Leis as mentioned in this paper gave an account of some recent developments in the theory of partial differential equations for readers thoroughly familiar with functional analysis, dealing with various types of problem for the wave equation, Maxwell's equations, Schrodinger's equation, the plate equation etc.
Journal ArticleDOI
Wave-number-explicit bounds in time-harmonic scattering
TL;DR: This paper considers the problem of scattering of time-harmonic acoustic waves by a bounded, sound soft obstacle in two and three dimensions, studying dependence on the wave number in two clas...
Journal ArticleDOI
A uniqueness result for scattering by infinite rough surfaces
Simon N. Chandler-Wilde,Bo Zhang +1 more
TL;DR: It is shown in this paper that the boundary value problem for the scattered field has at most one solution, and it is proved existence of solution and a limiting absorption principle.
Journal ArticleDOI
Integral equation methods for scattering by infinite rough surfaces
Bo Zhang,Simon N. Chandler-Wilde +1 more
TL;DR: In this article, the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane were considered and two boundary integral equation formulations were proposed.
Journal ArticleDOI
Variational Approach in Weighted Sobolev Spaces to Scattering by Unbounded Rough Surfaces
TL;DR: Well-posedness of this variational formulation in an energy space with weights is proved, which extends previous results in the unweighted setting to more general inhomogeneous terms in the Helmholtz equation.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
Book
Integral equation methods in scattering theory
David Colton,Rainer Kress +1 more
TL;DR: In this article, the Riesz-Fredholm theory for compact operators is applied to boundary-value problems for the scalar Helmholtz equation and the time-harmonic Maxwell equations.
Book
Initial Boundary Value Problems in Mathematical Physics
TL;DR: In this paper, the authors present an introduction both to classical scattering theory and to the time-dependent theory of linear equations in mathematical physics, using Hibert space methods to develop the latter theory in such a way that the asymptotic behaviour of large time can be discussed.