Electron. J. Diff. Equ., Vol. 2015 (2015), No. 142, pp. 1-11.

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

Celene Buriol, Marcio V. Ferreira

Abstract:
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.

Submitted June 30, 2014. Published May 21, 2015.
Math Subject Classifications: 35Q61, 35Q79, 35B40.
Key Words: Maxwell equation; orthogonal decomposition; exponential decay.

Show me the PDF file (223 KB), TEX file, and other files for this article.

Celene Buriol
Department of Mathematics
Federal University of Santa Maria
Santa Maria, CEP 97105-900, RS, Brazil
email: celene@smail.ufsm.br
Marcio V. Ferreira
Department of Mathematics
Federal University of Santa Maria
Santa Maria, CEP 97105-900, RS, Brazil
email: marcio.ferreira@ufsm.br

Return to the EJDE web page