Differential and Integral Equations

An identification problem for the Maxwell equations in a non-homogeneous dispersive medium

Cecilia Cavaterra and Alfredo Lorenzi

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We consider the propagation of electromagnetic waves in a non-homogeneous medium. The related constitutive relations contain time and space dependent convolution kernels. Since they are a priori unknown, a basic question concerns their identification. In the present paper, this is obtained by reducing the problem to a system of nonlinear integral equations of the second kind. Via a Contraction Theorem, we prove local (in time) existence and uniqueness results. Lipschitz continuous dependence upon the data is also proved.

Article information

Differential Integral Equations, Volume 8, Number 5 (1995), 1167-1190.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R30: Inverse problems
Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 78A25: Electromagnetic theory, general


Cavaterra, Cecilia; Lorenzi, Alfredo. An identification problem for the Maxwell equations in a non-homogeneous dispersive medium. Differential Integral Equations 8 (1995), no. 5, 1167--1190. https://projecteuclid.org/euclid.die/1369056050

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