Book Details
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
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.
Part 1. MODELLING AND MATHEMATICAL PRELIMINARIES
Chapter 1. Complex Media
Chapter 2. The Maxwell Equations and Constitutive Relations
Chapter 3. Space and Operators
Part 2. TIME-HARMONIC DETERMINISTIC PROBLEMS
Chapter 4. Well Posedness
Chapter 5. Scattering Problems: Beltrami Fields and Solvability
Chapter 6. Scattering Problems: A Variety of Topics
Part 3. TIME-DEPENDENT DETERMINISTIC PROBLEMS
Chapter 7. Well Posedness
Chapter 8. Controllability
Chapter 9. Homogenisation
Chapter 10. Towards a Scattering Theory
Chapter 11. Nonlinear Problems
Chapter 12. Well Posedness
Chapter 13. Controllability
Chapter 14. Homogenisation
Part 5. APPENDICES
Appendix A. Some Facts from Functional Analysis
Appendix B. Some Facts from Stochastic Analysis
Appendix C. Some Facts from Elliptic Homogenisation Theory
Appendix D. Some Facts form Dyadic Analysis
Appendix E. Notation and abbreviations
Bibliography
Index
A FIRST COURSE IN DIMENSIONAL ANALYSIS : SIMPLIFYING COMPLEX PHENOMENA USING
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