Energy decay for Maxwell's equations with Ohm's law in partially cubic domains

Kim Dang Phung

doi:10.3934/cpaa.2013.12.2229

Article Contents

2013, Volume 12, Issue 5: 2229-2266. Doi: 10.3934/cpaa.2013.12.2229

This issue Previous Article Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation Next Article Convexity of solutions to boundary blow-up problems

Energy decay for Maxwell's equations with Ohm's law in partially cubic domains

Kim Dang Phung^1,

1.
Université d'Orléans, Laboratoire MAPMO, CNRS UMR 7349, Fédération Denis Poisson, FR CNRS 2964, Bâtiment de Mathématiques, B.P. 6759, 45067 Orléans Cedex 2

Received: December 31, 2011

Revised: May 31, 2012

Published: August 2013

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Abstract

We prove a polynomial energy decay for the Maxwell's equations with Ohm's law in partially cubic domains with trapped rays. We extend the results of polynomial decay for the scalar damped wave equation in partially rectangular or cubic domain. Our approach have some similitude with the construction of reflected gaussian beams.

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Mathematics Subject Classification: Primary: 35B40, 35Q61; Secondary: 93D15.

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