BOUNDARY-VALUE PROBLEMS FOR THE MAXWELL'S EQUATIONS

Abstract

This report contains the proofs of the uniqueness and existence theorems for an electromagnetic field when the normal component of both the electric and magnetic fields are given on a smooth surface. The truth of the above theorems was suggested by V. Rumsey. The results are obtained for an exterior domain. However, the same method can be used for the interior problems. Whereas one synthesizes an electromagnetic field by a surface current when either the tangential electric or magnetic field is given, we synthesize our electromagnetic field by means of the electric and magnetic surface charges. We also show that solutions to Maxwell's equations can be expressed in terms of solutions to a second order partial differential equation in certain coordinate systems when the parameters E and mu are allowed to have a certain anisotropic property. This result represents an extension of those obtained by C. Mueller and by P. Friedman.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1963
Accession Number
AD0401209

Entities

People

  • Kane Yee

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Advanced Electronics
  • Air Platforms

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Cartesian Coordinates
  • Coordinate Systems
  • Dielectric Permittivity
  • Differential Equations
  • Electric Fields
  • Electromagnetic Fields
  • Electromagnetism
  • Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Magnetic Fields
  • Partial Differential Equations
  • Radiation
  • Scalar Functions
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Mathematical Modeling and Probability Theory.
  • Plasma Physics / Magnetohydrodynamics