Mathematical Problems of Classical Nonlinear Electromagnetic Theory

, by Bloom; Frederick

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ISBN: 9780582210219 | 0582210216
Cover: Hardcover
Copyright: 2/8/1993

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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 Theory	p. 1
Electrostatics and Dielectric Media	p. 2
Electric Currents and Electromagnetic Induction	p. 10
Maxwell's Equations and the Propagation of Electromagnetic Waves	p. 23
Transmission Lines: Basic Concepts	p. 38
Wave-Dielectric Interactions I: Formation of Singularities	p. 48
Hyperbolic Systems and Conservation Laws	p. 49
Shock Formation: Single Equations in One Space Dimension	p. 54
Weak Solutions of Hyperbolic Conservation Laws	p. 58
Riemann Invariants and Genuine Nonlinearity	p. 67
Shock Formation in 2 x 2 Systems	p. 71
Basic Equations for Wave-Dielectric Interactions	p. 74
Shock Formation in Dielectrics	p. 78
Multidimensional Problems: Shock Formation	p. 104
Wave-Dielectric Interactions II: Growth Estimates and Existence of Smooth Solutions	p. 110
Logarithmic Convexity and Concavity	p. 112
Growth Estimates for Wave-Dielectric Interactions: Differential Inequalities	p. 117
Growth Estimates for Wave-Dielectric Interactions: Riemann Invariants	p. 129
Global Existence for Small Data: An Example	p. 148
Global Existence of Solutions in the Wave-Dielectric Interaction Problem	p. 151
A Model of Superconductivity in a Nonlinear Dielectric	p. 172
Multidimensional and Nonstrictly Hyperbolic Problems Governing Wave-Dielectric Interactions	p. 190
Distributed Parameter Nonlinear Transmission Lines I: Shock Formation and Existence of Smooth Solutions	p. 195
Shock Formation in Nonlinear Transmission Lines	p. 197
Global Existence with Small Data: Riemann Invariants Arguments	p. 214
Global Existence with Small Data: Energy Estimates	p. 242
Distributed Parameter Nonlinear Transmission Lines II: Existence of Weak Solutions	p. 263
Weak Solutions of the Burgers' Equation I	p. 265
The Concept of the Young Measure	p. 270
Weak Solutions of the Burgers' Equation II	p. 276
Systems of Conservation Laws and DiPerna's Theorem	p. 282
The Nonlinear Transmission Line: Some Preliminaries	p. 291
The Regularized Transmission Line: Existence, Uniqueness, and Uniform Boundedness of Solutions	p. 297
Existence of Global Weak Solutions for the Transmission Line	p. 311
Some Nonlocal Electromagnetic Problems	p. 320
Equilibrium States of an Elastic Conductor in a Magnetic Field: Non-Self Interaction Case	p. 322
The Self-Interacting Current Bearing Wire	p. 329
Self-Interacting Wires: Existence of Straight Equilibrium States	p. 331
Self-Interacting Wires: Existence of Plane Circular States	p. 334
Helical States of Self-Interacting Wires	p. 341
Perturbations of Equilibrium States of Self-Interacting Current Bearing Wires	p. 350
Nonlocal Problems for Conducting Bodies	p. 357
Bibliography	p. 375
Table of Contents provided by Blackwell. All Rights Reserved.

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Mathematical Problems of Classical Nonlinear Electromagnetic Theory

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Mathematical Problems of Classical Nonlinear Electromagnetic Theory

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