Well-posedness and exponential stability of Maxwell-like systems coupled with strongly absorbing layers

This work deals with a family of PDEs which are derived from the Maxwell system set into an anisotropic medium. The system consists of four coupled linear equations. The first two correspond to the Maxwell system perturbed by zero-order operators which are represented by diagonal tensors with compact support. The last two equations are ODEs. Each system is written in a bounded domain and its boundary is modelled by a Silver–Muller condition. Firstly we establish that each problem is well-posed, providing the tensors are positive with bounded terms in Ω. Secondly we address the question of the long-time stability of each model. We prove that there exists a functional of energy which is exponentially decreasing if the domain is strictly star-shaped.

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