Global well-posedness and exponential stability for Maxwell's equations under delayed boundary condition in metamaterials

Abstract

We develop an initial-boundary value problem derived from the Maxwell's system with a nonlinear feedback-type boundary mechanism in metamaterials, which both involves polarization, magnetization effect and time-localized delay effect in a bounded domain. Based on the nonlinear semigroup theory and the properties of viscoelasticity theory, we show the well-posedness of solution in an appropriate Hilbert space. Under some suitable assumptions and geometric conditions, we prove the exponential stability of the Maxwell's system.