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Boundary stabilization of Maxwell’s equations. (Stabilisation frontière des équations de Maxwell.) (French. Abridged English version) Zbl 0861.35114

Summary: We consider Maxwell’s equations with the Silver-Müller absorbing boundary conditions in a bounded domain of \(\mathbb{R}^3\). Assuming that the domain is star-shaped we prove the exponential energy decay of the solutions. As a consequence, we improve some earlier exact controllability theorems by weakening their time assumptions. Our results are optimal if \(\Omega\) is a ball. The proofs are based on a new identity obtained by the multiplier method.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
35B37 PDE in connection with control problems (MSC2000)
35B35 Stability in context of PDEs
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