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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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(p.163) Chapter Eight Controllability
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Princeton University Press

This chapter presents some issues concerning the controllability of the Maxwell equations for complex media in the time domain. It uses a fixed point approach, which is based on the controllability problem for the Maxwell equations and which treats the integrodifferential terms in the constitutive relations for the complex media as a perturbation. The chapter also presents some results on the controllability of the Maxwell system that are essential in the study of the controllability problem in complex media. Details on the solution of the controllability problem are provided. And though the main approach of this chapter is a constructive one, it also provides an abstract approach to controllability based on semigroup arguments. Moreover, the chapter briefly discusses the problem of boundary controllability as well as the problem of optimal control for Maxwell equations. Finally, miscellaneous results concerning controllability for time-harmonic problems are presented.

Keywords:   controllability, Maxwell equations, fixed point approach, controllability problem, semigroup arguments, boundary controllability, Hilbert Uniqueness method

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