Geodesic
Orthogonal decomposition and asymptotic behavior for a linear coupled system of Maxwell and heat equations
Electronic journal of differential equations, Tome 2015 (2015)
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.
Classification : 35Q61, 35Q79, 35B40
Keywords: Maxwell equation, orthogonal decomposition, exponential decay 
@article{EJDE_2015__2015__a80,
     author = {Buriol,  Celene and Ferreira,  Marcio},
     title = {Orthogonal decomposition and asymptotic behavior for a linear coupled system of {Maxwell} and heat equations},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1321.35222},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a80/}
}
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JO  - Electronic journal of differential equations
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%A Ferreira,  Marcio
%T Orthogonal decomposition and asymptotic behavior for a linear coupled system of Maxwell and heat equations
%J Electronic journal of differential equations
%D 2015
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%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a80/
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%F EJDE_2015__2015__a80
Buriol,  Celene; Ferreira,  Marcio. Orthogonal decomposition and asymptotic behavior for a linear coupled system of Maxwell and heat equations. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a80/