Energy methods for a parabolic-hyperbolic interface problem arising in electromagnetism
Abstract
We consider a two-dimensional 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 three-dimensional 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