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This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…

Analysis of PDEs · Mathematics 2023-12-08 Heping Dong , Peijun Li

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…

Mathematical Physics · Physics 2011-11-10 Ole Henrik Waagaard , Johannes Skaar

Consider a broken geodesics $\alpha([0,l])$ on a compact Riemannian manifold $(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for…

Analysis of PDEs · Mathematics 2007-05-23 Yaroslav Kurylev , Matti Lassas , Gunther Uhlmann

This paper develops a trace-regular variational framework for time-harmonic Maxwell scattering problems involving pointwise nonlinear boundary and interface responses. We investigate three canonical classes of models: nonlinear impedance,…

Analysis of PDEs · Mathematics 2026-05-26 Chao Deng , Yixian Gao

We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…

Classical Physics · Physics 2016-05-04 Dionisios Margetis , Mitchell Luskin

In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…

Analysis of PDEs · Mathematics 2023-11-21 Tomáš Dohnal , Mathias Ionescu-Tira , Marcus Waurick

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

An inverse scattering problems for the 3-D generalized Helmholtz equation is considered. Only the modulus of the complex valued scattered wave field is assumed to be measured and the phase is not measured. Uniqueness theorem is proved.

Mathematical Physics · Physics 2016-07-15 Michael V. Klibanov

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

Analysis of PDEs · Mathematics 2018-12-03 Heping Dong , Jun Lai , Peijun Li

We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…

Analysis of PDEs · Mathematics 2022-07-01 Xuezhu Lu

This paper is concerned with the uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency. It can be proved that the unknown…

Analysis of PDEs · Mathematics 2023-07-25 Xiaoxu Xu

The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein…

Analysis of PDEs · Mathematics 2014-01-27 Willie Wai-Yeung Wong , Pin Yu

The paradox of the divergence of the resonant scattering cross section of a cylinder with the permittivity equals minus unity and vanishing radius (R) irradiated by a monochromatic electromagnetic wave is discussed. Within the framework of…

Optics · Physics 2019-07-24 Yaroslav A. Brynkin , Michael I. Tribelsky

In this work we develop an Almgren type monotonicity formula for a class of elliptic equations in a domain with a crack, in the presence of potentials satisfying either a negligibility condition with respect to the inverse-square weight or…

Analysis of PDEs · Mathematics 2020-07-16 Alessandra De Luca , Veronica Felli

We review the proof of existence and uniqueness of solutions of the Maxwell-Schr"odinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined in terms of asymptotic data, without any restriction on the…

Analysis of PDEs · Mathematics 2008-04-04 J. Ginibre , G. Velo

Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…

Analysis of PDEs · Mathematics 2013-11-26 Guillaume Bal

We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…

Mathematical Physics · Physics 2020-07-14 Christian Daveau , Abdessatar Khelifi , Houssem Lihiou

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…

Analysis of PDEs · Mathematics 2021-11-24 Jianli Xiang , Guanghui Hu

The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the field of inverse problems, because of its fundamental role in…

This work is on the numerical approximation of incoming solutions to Maxwell's equations with dissipative boundary conditions whose energy decays exponentially with time. Such solutions are called asymptotically disappearing (ADS) and they…

Numerical Analysis · Mathematics 2013-07-23 James H. Adler , Vesselin Petkov , Ludmil T. Zikatanov