Exponential decay of the linear Maxwell system due to conductivity near the boundary

Richard Nutt; Roland Schnaubelt

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arXiv · 2601.09502

Exponential decay of the linear Maxwell system due to conductivity near the boundary

Richard Nutt·Roland Schnaubelt

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Abstract

We study the anisotropic linear Maxwell system on a bounded domain $\Omega$ with perfectly conducting boundary conditions. It is damped via a conductivity $\sigma$ which is strictly positive on a collar at the boundary. We prove that solutions decay exponentially to 0, if the fields have no magnetic charges on $\Omega$ and no electric charges off the support of $\sigma$. Our approach relies on a splitting of the solution via a Helmholtz decomposition and an observability-type estimate for a related second-order system without charges, shown using Morawetz multipliers. Corresponding exact observability and controllability results are also established.

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Richard Nutt, Roland Schnaubelt. 2026-01-14. Exponential decay of the linear Maxwell system due to conductivity near the boundary. https://arxiv.org/abs/2601.09502

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