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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This study investigates the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. The results demonstrate the existence of solutions for small data, which decay exponentially to 0. The improvement in results is achieved by introducing a new trace estimate, an observability-type estimate, and a detailed regularity analysis.