A small domain limit for nonlinear dielectric media
on (0, oo) x G. Here C R3 denotes the spatial domain and G C O is an open subset. The unknown functions are the electric and magnetic fields E, H, which depend on the time t > 0 and the space-variable x G 12, arid the dielectric polarization P defined on M+ x G. In 1.1, the function P is the extension of P on R+ x V. defined by zero on the set R+ x (fl\G). This system, which describes the propagation of electromagnetic waves in a dielectric medium occupying the set G, is supplemented by the initial boundary conditions nAE = 0on (O.oo) xl\ and n A H = 0 on (0, oo) x T2 (1.3) E(0, x) = E0(x). H(0, x) = H0(x) (1.4) and P(0, x) = P(1(a:), <9#P(0, x) = Pi(x) oil G. (1-5)