Well-posedness of the Cauchy problem associated with Bérenger’s system. (Caractère bien posé du problème de Cauchy pour le système de Bérenger.) (French. Abridged English version) Zbl 0928.35176

Métral, Jérôme; Vacus, Olivier

C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 10, 847-852 (1999).

Summary: The Bérenger perfectly matched layer is used in computational electromagnetism as an absorbing layer in scattering problems. It raises delicate mathematical issues. In this note we show, for regular data, the existence and uniqueness of strong solutions to the Cauchy problem derived from the PML method. The result is presented in the 2-D case. The key to the proof is an appropriate control of a mixed \(H^1-L^2\) norm of the solution by the same norm of the initial data. A subsequent paper is in preparation about extensions of this results \((L^2\) estimates, 3-D case).

MSC:

35Q60	PDEs in connection with optics and electromagnetic theory
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

Keywords:

Maxwell’s equations; existence and uniqueness of strong solutions to the Cauchy problem; PML method