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*Electromagnetics-Modelling, Simulation, Control and Industrial Applications*was held at Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin during May 13-17, 2013. Organizers of this workshop were Dietmar Hömberg (WIAS), Ronald H. W. Hoppe (University of Augsburg/University of Houston), Olaf Klein (WIAS), Jürgen Sprekels (WIAS) and Fredi Tröltzsch (Technical University of Berlin). More than sixty researchers from mathematical, physical, engineering and industrial communities participated in this scientific meeting. This special issue of DCDS-S, which contains eleven research-level articles, is based on the talks presented during the workshop. Electromagnetism plays an important role in many modern high-technological applications. Our workshop brought together prominent worldwide experts from academia and industry to discuss recent achievements and future trends of modelling, computations and analysis in electromagnetics. The contributions to this volume cover the following topics: finite and boundary element discretization methods for the electromagnetic field equations in frequency and time domain, optimal control and model reduction for multi-physics problems involving electromagnetics, mathematical analysis of Maxwell's equations as well as direct and inverse scattering problems.

We particularly emphasize that most articles are devoted to mathematically challenging issues in applied sciences and industrial applications. The optimal control and model reduction presented by S. Nicaise et al. arise from electromagnetic flow measurement in the real world. The contribution by G. Beck et al. focuses on a generalized telegrapher's model which describes the propagation of electromagnetic waves in non-homogeneous conductor cables with multi-wires. The numerical analysis of boundary integral formulations carried out by K. Schmidt et al. is motivated by asymptotic models for thin conducting sheets. The integral equation system established by B. Bugert et al. and the analysis and experiments performed by H. Gross et al. make new contributions to direct and inverse electromagnetic scattering from diffraction gratings, respectively. The locating and inversion schemes for detecting unknown configurations proposed by H. Ammari, G. Bao, J. Li and X. Liu et al. could be important and useful in radar and medical imaging, non-destructive testing and geophysical exploration. Last but not least, one can also find important mathematical applications regarding the estimate of the second Maxwell eigenvalues obtained by D. Pauly and the regularity of solutions to Maxwell's system at low frequencies due to P-E. Druet.

We hope the presented papers will find a large audience and they may stimulate novel studies on electromagnetism. Finally we would like to express our gratitude to the Research Center MATHEON and the Weierstrass Institute, whose financial support made the workshop possible.

We study the problem of determining uniquely a time-dependent singular potential $q$, appearing in the wave equation $\partial_t^2u-Δ_x u+q(t,x)u = 0$ in $Q = (0,T)×Ω$ with $T>0$ and $Ω$ a $ \mathcal C^2$ bounded domain of $\mathbb{R}^n$, $n≥2$. We start by considering the unique determination of some general singular time-dependent coefficients. Then, by weakening the singularities of the set of admissible coefficients, we manage to reduce the set of data that still guaranties unique recovery of such a coefficient. To our best knowledge, this paper is the first claiming unique determination of unbounded time-dependent coefficients, which is motivated by the problem of determining general nonlinear terms appearing in nonlinear wave equations.

This paper concerns inverse source problems for the time-dependent Maxwell equations. The electric current density is assumed to be the product of a spatial function and a temporal function. We prove uniqueness and stability in determining the spatial or temporal function from the electric field, which is measured on a sphere or at a point over a finite time interval.

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