The Initial Boundary Problem for the Maxwell Equations in the Presence of a Moving Body
- 1 November 1985
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 16 (6) , 1165-1179
- https://doi.org/10.1137/0516086
Abstract
Existence and uniqueness of finite energy solutions of the Maxwell equations is proved in the presence of a moving body which may be either a perfect conductor or a dielectric. For the perfect conductor, it is assumed that the speed of the body is less than the speed of propagation in a vacuum, while for the dielectric it is assumed that the speed of the body is less than the speed of propagation within the body when at rest. The proof involves localization of the problem to a neighborhood of the moving boundary and a change of coordinates using the techniques of general relativity. The Neumann problem for a moving body and the scalar wave equation is also treated.Keywords
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