EXISTENCE, ORTHOGONAL DECOMPOSITION AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF A SYSTEM IN ELECTROMAGNETISM
DOI:
https://doi.org/10.5902/2179460X12251Keywords:
Maxwell’s equations, orthogonal decomposition, exponential decay.Abstract
http://dx.doi.org/10.5902/2179460X12251
In this paper we consider a system of Maxwell’s equations, which models the propagation of electromagnetic waves in a boundedregion of R3. First we prove the existence and uniqueness of a solution of such a system using, for this, theory of Semigroupof linear operators. We obtain, then, the orthogonal decomposition of the electromagnetic field. Finally, using that orthogonaldecomposition and choosing an appropriate multiplier, we show that the total energy of the system decays exponentially to zero ast ! ¥. The method presented in this paper is quite different from those that appear in the literature related to this subject.
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