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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Determ<strong>in</strong>istic problems: Modell<strong>in</strong>g<br />
The Maxwell system as an IVP<br />
The constitutive relations are now modelled by an operator L <strong>and</strong> are<br />
understood as the functional equation<br />
d = Lu.<br />
The properties of this operator reflect the physical properties of the<br />
medium <strong>in</strong> question.<br />
So the Maxwell system can be written as an IVP for an abstract evolution<br />
equation<br />
(Lu) ′ (t) = Mu(t) + j(t) , for t > 0 ,<br />
(8)<br />
u(0) = u0 .<br />
The prime st<strong>and</strong>s for the time derivative.<br />
The equation <strong>in</strong> the IVP (28) is an <strong>in</strong>homogeneous neutral functional<br />
differential equation.<br />
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 14 / 95
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