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Abstract

Let $Ω = R^{3} ∖ \bar{K}$ , where K is an open bounded domain with smooth boundary Γ. Let $V (t) = e^{t G_{b}}$ , $t ⩾ 0$ , be the semigroup related to Maxwell’s equations in Ω with dissipative boundary condition $ν \land (ν \land E) + γ (x) (ν \land H) = 0$ , $γ (x) > 0$ , $\forall x \in Γ$ . We study the case when $γ (x) \neq 1$ , $\forall x \in Γ$ , and we establish a Weyl formula for the counting function of the eigenvalues of $G_{b}$ in a polynomial neighbourhood of the negative real axis.

Keywords

Dissipative boundary conditions dissipative eigenvalues Weyl formula

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Asymptotic of the dissipative eigenvalues of Maxwell’s equations

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