Stability of the anisotropic Maxwell equations with a conductivity term

Matthias Eller

doi:10.3934/eect.2019018

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2019, Volume 8, Issue 2: 343-357. Doi: 10.3934/eect.2019018

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Stability of the anisotropic Maxwell equations with a conductivity term

Matthias Eller

Department of Mathematics, Georgetown University, Washington, DC 20057, USA

Received: April 30, 2018

Revised: August 31, 2018

Early access: March 2019

Published: May 2019

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Abstract

The dynamic Maxwell equations with a conductivity term are considered. Conditions for the exponential and strong stability of an initial-boundary value problem are given. The permeability and the permittivity are assumed to be $ 3\times 3 $ symmetric, positive definite tensors. A result concerning solutions of higher regularity is obtained along the way.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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