Electromagnetism of Continuous Media Mathematical Modelling and Applications [Hardcover]

The wide application of techniques in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (i.e. materials with 'memory'). Of equal importance is the understanding of the physical behavior of these materials and consequently developing mathematical modelling techniques for prediction. This self contained text discusses the mathematical modelling used with these types of electromagnetic materials. It provides a carefully structured, coherent and comprehensive treatment of electromagnetism of continuous media. The authors provide a systematic review of known subjects along with original results about thermodynamics of electromagnetic materials, well-posedness of initial boundary-value problems, variational settings, and wave propagation. Models of non-linear materials, non-local materials (superconductors), and hysteretic (magnetic) materials are also developed in detail.

Preface
1.Part I: Basic Notions in ElectromagnetismElectromagnetic fields
2. Green's functions and retarded potentials
3. Time-harmonic fields
4. Models of materials with memory
5.Part II: Thermodynamics and Mathematical ProblemsThermodynamics of simple electromagnetic systems
6. Thermoelectromagnetic systems
7. Existence and uniqueness
8. Wave propagation
9. Extremum principles
10.Part III: Nonlinearity and NonlocalityProblems in nonlinear electromagnetism
11. Nonlocal electromagnetism and superconductivity
12. Magnetic hysteresis
A.AppendicesSome properties of Bessel functions
B. Fourier transforms and Sobolev spaces
C. Compact operators and eigenfunctions
D. Differential operators in curvilinear coordinates
E. Finite formulation of electromagnetism