Electromagnetics in deterministic and stochastic bianisotropic media
Electromagnetics in deterministic and stochastic bianisotropic media
Electromagnetics in deterministic and stochastic bianisotropic media
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Time-doma<strong>in</strong> problems<br />
Time-doma<strong>in</strong> problems: Well-posedness<br />
Several alternative approaches to the solvability of the IVP for the Maxwell<br />
system<br />
(Lu) ′ (t) = Mu(t) + j(t) , for t > 0 ,<br />
(28)<br />
u(0) = u0 ,<br />
supplemented with the constitutive relations for dissipative <strong>bianisotropic</strong><br />
<strong>media</strong><br />
� t<br />
(Lu)(t, x) = Aor(x)u(t, x) + Gd(t − s, x)u(s, x) ds , (29)<br />
0<br />
can be considered, e.g., semigroups, evolution families, the Faedo–Galerk<strong>in</strong><br />
method.<br />
We adopt the former, based on the semigroup generated by the Maxwell<br />
operator. Then the convolution terms are treated as perturbations of this<br />
semigroup.<br />
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 34 / 95
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