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arXiv · 2601.09490

Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary

Richard Nutt·Roland Schnaubelt
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Abstract

We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a nontrapping condition. Our approach relies on a new trace estimate for the corresponding non-autonomous linear problem, an observability-type estimate, and a detailed regularity analysis. The results are improved in the linear autonomous case, using properties of the Helmholtz decomposition in Sobolev spaces of (small) negative order.

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Richard Nutt, Roland Schnaubelt. 2026-01-14. Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary. https://doi.org/10.1016/j.jmaa.2023.127915

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