Electromagnetics in deterministic and stochastic bianisotropic media

Time-domain problems
Controllability Problems
The governing equation
(A oru + G d ⋆ u) ′ = Mu + j, (30)
can be simplified if we assume that Gd(t, x) is weakly differentiable with
respect to the temporal variable. Then we may differentiate the
convolution integral, and by multiplying to the right by A−1 or we get
where
u ′ = M Au + G A ⋆ u + J A, (31)
G A := −A −1
or G ′ d , M A := A −1
or M , J A := A −1
or j,
and we have assumed that G d(0, x) = 0.
The boundary conditions, as well as the divergence free character of the
electromagnetic field, can be included in the definition of the operator M
in appropriately selected function spaces.
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 38 / 95