A new family of first-order boundary conditions for the Maxwell system: Derivation, well-posedness and long-time behavior
This paper studies the time-dependent Maxwell system in the case of TE-polarized electromagnetic waves subject to a family of first-order local boundary conditions. The conditions differ from an arbitrary function and all of them lead to a well-posed mixed problem capable of description in terms of a continuous semigroup. By involving an invariant space for the Maxwell system, the limit state is shown to be capable of explicit description as a solution to a boundary-value problem dependent on the initial data. The long time behavior of the solution is also analyzed in detail.
scientific article; zbMATH DE number 1975976