Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary
arXiv:2601.09490 · doi:10.1016/j.jmaa.2023.127915
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 . 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.