arXiv subjects

Richard Nutt

Publications and source records attributed to Richard Nutt.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

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

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.

math.AP↗