Komornik, Vilmos Boundary stabilization of Maxwell’s equations. (Stabilisation frontière des équations de Maxwell.) (French. Abridged English version) Zbl 0861.35114 C. R. Acad. Sci., Paris, Sér. I 318, No. 6, 535-540 (1994). 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. Cited in 4 Documents 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 Keywords:Maxwell’s equations; Silver-Müller absorbing boundary conditions; exponential energy decay; exact controllability PDFBibTeX XMLCite \textit{V. Komornik}, C. R. Acad. Sci., Paris, Sér. I 318, No. 6, 535--540 (1994; Zbl 0861.35114)