Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach; I. G. Stratis; A. N. Yannacopoulos

G. F. Roach, I. G. Stratis and A. N. Yannacopoulos

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

In: Princeton Series in Applied Mathematics, 42

Princeton University Press | 2012

https://doi.org/10.1515/9781400842650

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Contents

About this book

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.

Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Author information

G. F. Roach is professor emeritus in the Department of Mathematics and Statistics at the University of Strathclyde. I. G. Stratis is professor in the Department of Mathematics at the National and Kapodistrian University, Athens. A. N. Yannacopoulos is professor in the Department of Statistics at the Athens University of Economics and Business.

Reviews

This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems.---Vilmos Komornik, Mathematical Reviews

"This is an outstanding book that has the potential to become a real classic. It is the first to systematically address the mathematics of electromagnetic wave propagation in complex media. It will be useful not only to mathematicians but also graduate students, physicists, and engineers who want to get a state-of-the-art picture of scattering by complex media."—Gerhard Kristensson, Lund University, Sweden

Frontmatter Free access PDF PDF	i
Contents Free access PDF PDF	vii
Preface Access restricted Content is available PDF PDF	xi
Part 1. Modelling and Mathematical Preliminaries
Chapter One. Complex Media Access restricted Content is available PDF PDF	3
Chapter Two. The Maxwell Equations and Constitutive Relations Access restricted Content is available PDF PDF	9
Chapter Three. Spaces and Operators Access restricted Content is available PDF PDF	38
Part 2. Time-Harmonic Deterministic Problems
Chapter Four. Well Posedness Access restricted Content is available PDF PDF	61
Chapter Five. Scattering Problems: Beltrami Fields and Solvability Access restricted Content is available PDF PDF	83
Chapter Six. Scattering Problems: A Variety of Topics Access restricted Content is available PDF PDF	112
Part 3. Time-Dependent Deterministic Problems
Chapter Seven. Well Posedness Access restricted Content is available PDF PDF	151
Chapter Eight. Controllability Access restricted Content is available PDF PDF	163
Chapter Nine. Homogenisation Access restricted Content is available PDF PDF	180
Chapter Ten. Towards a Scattering Theory Access restricted Content is available PDF PDF	212
Chapter Eleven. Nonlinear Problems Access restricted Content is available PDF PDF	231
Part 4. Stochastic Problems
Chapter Twelve. Well Posedness Access restricted Content is available PDF PDF	247
Chapter Thirteen. Controllability Access restricted Content is available PDF PDF	263
Chapter Fourteen. Homogenisation Access restricted Content is available PDF PDF	275
Part 5. Appendices
Appendix A. Some Facts from Functional Analysis Access restricted Content is available PDF PDF	293
Appendix B. Some Facts from Stochastic Analysis Access restricted Content is available PDF PDF	316
Appendix C. Some Facts from Elliptic Homogenisation Theory Access restricted Content is available PDF PDF	327
Appendix D. Some Facts from Dyadic Analysis George Dassios Access restricted Content is available PDF PDF	334
Appendix E. Notation and abbreviations Access restricted Content is available PDF PDF	341
Bibliography Access restricted Content is available PDF PDF	343
Index Access restricted Content is available PDF PDF	377
Backmatter Access restricted Content is available PDF PDF	383

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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

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