Asymptotic expansions for currents caused by small interface changes of an electromagnetic inclusion

DOI10.1080/00036811.2011.601601zbMath1302.35140OpenAlexW2094960191MaRDI QIDQ4908188

Habib Zribi

Publication date: 4 March 2013

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2011.601601

zbMATH Keywords

Helmholtz equationsmall perturbationsinterface problemfull-asymptotic expansions boundary integral method

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Asymptotic expansions of solutions to PDEs (35C20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (11)

An integral equation method for the Helmholtz problem in the presence of small anisotropic inclusions ⋮ Reconstructing small perturbations of an obstacle for acoustic waves from boundary measurements on the perturbed shape itself ⋮ Asymptotic expansion for solution of Maxwell equation in domain with highly oscillating boundary ⋮ Shape reconstructions by using plasmon resonances with enhanced sensitivity ⋮ Maxwell interface problems‐ existence and uniqueness of solutions for Maxwell's equations ⋮ An asymptotic expansion for perturbations in the displacement field due to the presence of thin interfaces ⋮ Boundary voltage perturbations resulting from small surface changes of a conductivity inclusion ⋮ Small perturbation of a surface: full Maxwell's equations ⋮ Small perturbations of an interface for elastostatic problems ⋮ Asymptotic expansions for the voltage potentials with two-dimensional and three-dimensional thin interfaces ⋮ Asymptotic expansion of the solution of a transmission problem for the Stokes system with a small boundary perturbation for an inclusion

Cites Work

• Reconstruction of small interface changes of an inclusion from modal measurements. II: The elastic case
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities
• Reconstructing small perturbations of scatterers from electric or acoustic far‐field measurements
• Layer potential techniques in spectral analysis. Part I: Complete asymptotic expansions for eigenvalues of the Laplacian in domains with small inclusions
• Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements
• Recovery of small perturbations of an interface for an elliptic inverse problem via linearization
• The determination of a discontinuity in a conductivity from a single boundary measurement
• An improved operator expansion algorithm for direct and inverse scattering computations
• Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area

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