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In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…

Analysis of PDEs · Mathematics 2018-12-24 Yu Zhao , Guanghui Hu , Baoqiang Yan

A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…

Computational Physics · Physics 2020-02-18 Johan Helsing , Anders Karlsson

We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…

Analysis of PDEs · Mathematics 2017-07-18 Gregory Eskin

We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited…

Numerical Analysis · Mathematics 2026-02-23 Eric Lindström , Larisa Beilina

In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…

Analysis of PDEs · Mathematics 2020-12-07 Gen Nakamura , Manmohan Vashisth , Michiyuki Watanabe

This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…

Analysis of PDEs · Mathematics 2020-02-21 Peijun Li , Xu Wang

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…

Analysis of PDEs · Mathematics 2022-02-09 Victor Isakov , Shuai Lu , Boxi Xu

We give a survey of author's results on the inverse hyperbolic problems with time-dependent and time-independent coefficients. We consider the case of hyperbolic equations with Yang-Mills potentials and the case of domains with obstacles.…

Analysis of PDEs · Mathematics 2014-07-22 Gregory Eskin

We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ \epsilon(x)\partial_t u^m-\nabla\cdot\bigl(\gamma(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{in }(0,T)\times\Omega, \] where…

Analysis of PDEs · Mathematics 2026-03-10 Cătălin I. Cârstea , Tuhin Ghosh

This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain…

Numerical Analysis · Mathematics 2020-09-03 Marion Darbas , Jérémy Heleine , Stephanie Lohrengel

We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate…

Analysis of PDEs · Mathematics 2018-11-19 Bastian Harrach , Yi-Hsuan Lin , Hongyu Liu

We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…

Analysis of PDEs · Mathematics 2021-01-15 Gunther Uhlmann , Jian Zhai

We study time-dependent acoustic and electromagnetic waves governed by the scalar wave equation or Maxwell's equations in a bounded three-dimensional domain. We establish the existence of time-dependent boundary excitations that can be…

Analysis of PDEs · Mathematics 2026-03-03 Roland Griesmaier , Soumen Senapati

This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…

Analysis of PDEs · Mathematics 2026-04-15 Irina Kmit , Nataliya Protsakh , Viktor Tkachenko

For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…

Analysis of PDEs · Mathematics 2019-01-24 Sebastian Bauer , Dirk Pauly , Michael Schomburg

The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…

Classical Physics · Physics 2007-05-23 E. A. Matute

We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of…

Analysis of PDEs · Mathematics 2024-07-26 Boya Liu , Teemu Saksala , Lili Yan

This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…

Numerical Analysis · Mathematics 2023-01-04 Eleonora Denich , Paolo Novati , Stefano Picotti

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , O. Y. Imanuvilov , Masahiro Yamamoto

We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be $0, \infty$ or a finite…

Analysis of PDEs · Mathematics 2020-05-15 Huaian Diao , Hongyu Liu , Long Zhang , Jun Zou