Orthogonal decomposition and asymptotic behavior for a linear coupled system of Maxwell and heat equations

We study the asymptotic behavior in time of the solutions of a coupled system of linear Maxwell equations with thermal effects. We have two basic results. First, we prove the existence of a strong solution and obtain the orthogonal decomposition of the electromagnetic field. Also, choosing a suitabl...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2015; no. 142; pp. 1 - 11
Main Authors Celene Buriol, Marcio Ferreira
Format Journal Article
LanguageEnglish
Published Texas State University 21.05.2015
Subjects
exponential decay
Maxwell equation
orthogonal decomposition
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ISSN1072-6691

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Summary:We study the asymptotic behavior in time of the solutions of a coupled system of linear Maxwell equations with thermal effects. We have two basic results. First, we prove the existence of a strong solution and obtain the orthogonal decomposition of the electromagnetic field. Also, choosing a suitable multiplier, we show that the total energy of the system decays exponentially as $t \to + \infty$. The results obtained for this linear problem can serve as a first attempt to study other nonlinear problems related to this subject.
ISSN:1072-6691