Energy decay for Maxwell s equations with Ohm s law on partially cubic domains

Niveau: Secondaire, Lycée, Terminale
Energy decay for Maxwell?s equations with Ohm?s law on partially cubic domains Kim Dang Phung Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, Sichuan Province, China. E-mail: Abstract .- We prove a polynomial energy decay for the Maxwell?s equations with Ohm?s law on partially cubic domains with trapped rays. Keywords .- Maxwell?s equation; decay estimates; trapped ray. 1 Introduction The problems dealing with Maxwell?s equations with nonzero conductivity are not only theoretical interesting but also very important in many industrial applications (see e.g. [3], [7], [8]). Let be a bounded open connected region in R3, with a smooth boundary @ . We suppose that is simply connected and @ has only one connected component. The domain is occupied by an electromagnetic medium of constant electric permittivity o and constant magnetic permeability o. Let E and H denote the electric and magnetic ?elds respectively. The Maxwell?s equations with Ohm?s law are described by 8 >>>>< >>>>: o@tE curlH + E = 0 in [0;+1) o@tH + curlE = 0 in [0;+1) div (oH) = 0 in [0;+1) E = H = 0 on @ [0;+1) (E;H) (; 0) = (Eo;Ho) in .

• conductivity has


• scalar wave


• polynomial energy


• wave operator


• interpolation estimate


• has only


• unique solution


• estimate becomes


• energy decay