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Electromagnetic scattering for time-domain Maxwell’s equations in an unbounded structure

School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, Jilin 130024, P. R. China

E-mail Address: gaoyx643@nenu.edu.cn

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and

Peijun Li

Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

E-mail Address: lipeijun@math.purdue.edu

Corresponding author

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https://doi.org/10.1142/S0218202517500336Cited by:17 (Source: Crossref)

Abstract

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell’s equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an initial-boundary value problem in an infinite rectangular slab. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax–Milgram lemma, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the electric field by directly studying the time-domain Maxwell equations.

Communicated by A. Vasseur

Keywords:

AMSC: 35Q61, 78A25, 78M30

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