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-harmonic Problems – The Interior Problem<br />
Time-harmonic problems<br />
The study of time-harmonic problems for the Maxwell equations<br />
supplemented with the DBF constitutive relations is a well-developed area.<br />
The solvability of <strong>in</strong>terior <strong>and</strong> exterior BVPs is established by variational<br />
techniques, <strong>and</strong> their discretised versions are studied as well.<br />
The <strong>in</strong>terior problem reads<br />
curl E = βγ2E + iϖµ � γ �2 k H,<br />
curl H = βγ2H − iϖε � γ �2 <strong>in</strong> O, (18)<br />
k E,<br />
where ϖ > 0 is the angular frequency <strong>and</strong><br />
k 2 := ϖ 2 εµ , γ 2 := k 2 (1 − β 2 k 2 ) −1 . (19)<br />
These equations are complemented with the boundary condition<br />
n × E = f , on ∂O, (20)<br />
where f ∈ H −1/2 (div, ∂O) is a prescribed electric field on ∂O.<br />
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 24 / 95
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