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Mathematical Problems of Classical Nonlinear Electromagnetic Theory : Monographs and Surveys in Pure and Applied Mathematics - Frederick Bloom

Mathematical Problems of Classical Nonlinear Electromagnetic Theory

Monographs and Surveys in Pure and Applied Mathematics

Hardcover

Published: 8th February 1993
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A survey of some problems of current interest in the realm of classical nonlinear electromagnetic theory.

Preface
Elements of Classical Electromagnetic Theoryp. 1
Electrostatics and Dielectric Mediap. 2
Electric Currents and Electromagnetic Inductionp. 10
Maxwell's Equations and the Propagation of Electromagnetic Wavesp. 23
Transmission Lines: Basic Conceptsp. 38
Wave-Dielectric Interactions I: Formation of Singularitiesp. 48
Hyperbolic Systems and Conservation Lawsp. 49
Shock Formation: Single Equations in One Space Dimensionp. 54
Weak Solutions of Hyperbolic Conservation Lawsp. 58
Riemann Invariants and Genuine Nonlinearityp. 67
Shock Formation in 2 x 2 Systemsp. 71
Basic Equations for Wave-Dielectric Interactionsp. 74
Shock Formation in Dielectricsp. 78
Multidimensional Problems: Shock Formationp. 104
Wave-Dielectric Interactions II: Growth Estimates and Existence of Smooth Solutionsp. 110
Logarithmic Convexity and Concavityp. 112
Growth Estimates for Wave-Dielectric Interactions: Differential Inequalitiesp. 117
Growth Estimates for Wave-Dielectric Interactions: Riemann Invariantsp. 129
Global Existence for Small Data: An Examplep. 148
Global Existence of Solutions in the Wave-Dielectric Interaction Problemp. 151
A Model of Superconductivity in a Nonlinear Dielectricp. 172
Multidimensional and Nonstrictly Hyperbolic Problems Governing Wave-Dielectric Interactionsp. 190
Distributed Parameter Nonlinear Transmission Lines I: Shock Formation and Existence of Smooth Solutionsp. 195
Shock Formation in Nonlinear Transmission Linesp. 197
Global Existence with Small Data: Riemann Invariants Argumentsp. 214
Global Existence with Small Data: Energy Estimatesp. 242
Distributed Parameter Nonlinear Transmission Lines II: Existence of Weak Solutionsp. 263
Weak Solutions of the Burgers' Equation Ip. 265
The Concept of the Young Measurep. 270
Weak Solutions of the Burgers' Equation IIp. 276
Systems of Conservation Laws and DiPerna's Theoremp. 282
The Nonlinear Transmission Line: Some Preliminariesp. 291
The Regularized Transmission Line: Existence, Uniqueness, and Uniform Boundedness of Solutionsp. 297
Existence of Global Weak Solutions for the Transmission Linep. 311
Some Nonlocal Electromagnetic Problemsp. 320
Equilibrium States of an Elastic Conductor in a Magnetic Field: Non-Self Interaction Casep. 322
The Self-Interacting Current Bearing Wirep. 329
Self-Interacting Wires: Existence of Straight Equilibrium Statesp. 331
Self-Interacting Wires: Existence of Plane Circular Statesp. 334
Helical States of Self-Interacting Wiresp. 341
Perturbations of Equilibrium States of Self-Interacting Current Bearing Wiresp. 350
Nonlocal Problems for Conducting Bodiesp. 357
Bibliographyp. 375
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780582210219
ISBN-10: 0582210216
Series: Monographs and Surveys in Pure and Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 400
Published: 8th February 1993
Publisher: Taylor & Francis Ltd
Country of Publication: GB
Dimensions (cm): 27.9 x 21.6  x 2.2
Weight (kg): 0.64
Edition Number: 1