Energy methods for a parabolichyperbolic interface problem arising in electromagnetism
Abstract
We consider a twodimensional problem arising from the interaction of electromagnetic waves traveling in air with a metallic body. This problem leads to a parabolic equation inside the body and a hyperbolic equation outside; the two equations interact through jump relations across the boundary of the body. We prove the existence of solutions using energy estimates in conjunction with a Galerkin argument. We also remark on how to obtain similar results in the threedimensional case.
 Publication:

Zeitschrift Angewandte Mathematik und Physik
 Pub Date:
 November 1988
 DOI:
 10.1007/BF00945129
 Bibcode:
 1988ZaMP...39..931A
 Keywords:

 Electromagnetic Interactions;
 Energy Methods;
 Wave Propagation;
 Existence Theorems;
 Galerkin Method;
 Hyperbolic Differential Equations;
 Parabolic Differential Equations;
 Theorem Proving;
 Physics (General);
 Electromagnetic Wave;
 Mathematical Method;
 Parabolic Equation;
 Electromagnetism;
 Hyperbolic Equation