图书简介
The wide application of technologies in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (e.g materials with ’memory’). Of equal importance is the understanding of the physical behaviour 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.
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Preface; Part I: Basic Notions in Electromagnetism1: Electromagnetic fields; 2: Green’s functions and retarded potentials; 3: Time-harmonic fields; 4: Models of materials with memory; Part II: Thermodynamics and Mathematical Problems5: Thermodynamics of simple electromagnetic systems; 6: Thermoelectromagnetic systems; 7: Existence and uniqueness; 8: Wave propagation; 9: Extremum principles; Part III: Nonlinearity and Nonlocality10: Problems in nonlinear electromagnetism; 11: Nonlocal electromagnetism and superconductivity; 12: Magnetic hysteresis; AppendicesA: Some 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
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