# Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay

@article{Anikushyn2019GlobalWA, title={Global well-posedness and exponential stability for heterogeneous anisotropic Maxwell's equations under a nonlinear boundary feedback with delay}, author={Andrii Anikushyn and Michael Pokojovy}, journal={Journal of Mathematical Analysis and Applications}, year={2019} }

Abstract We consider an initial–boundary value problem for the Maxwell's system in a bounded domain with a linear nonhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver–Muller-type boundary feedback mechanism incorporating both an instantaneous damping and a time-localized delay effect. By proving the maximal monotonicity property of the underlying nonlinear generator, we establish the global well-posedness in an appropriate Hilbert space. Further, under suitable… Expand

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