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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics$
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G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Print publication date: 2012

Print ISBN-13: 9780691142173

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142173.001.0001

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The Maxwell Equations and Constitutive Relations

The Maxwell Equations and Constitutive Relations

Chapter:
(p.9) Chapter Two The Maxwell Equations and Constitutive Relations
Source:
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
Author(s):

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142173.003.0002

This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive relations are to be understood as operators connecting the electric flux density and the magnetic flux density with the electric and the magnetic fields. When they are introduced into the Maxwell equations, this chapter obtains differential equations (PDEs) that govern the evolution of the electromagnetic fields. This chapter also seeks to formulate and discuss the scope of the various problems related to the Maxwell equations that will be treated in this volume. It introduces and formulates in terms of differential equations various problems of interest related to the Maxwell equations: time-harmonic problems, scattering problems, time-domain evolution problems, random and stochastic problems, controllability problems, homogenisation problems, and others.

Keywords:   constitutive relations, Maxwell equations, mathematical modelling, complex electromagnetic media, electric flux density, magnetic flux density, differential equations, PDEs, electromagnetic fields

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