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arXiv · 2204.11779

Asymptotic of the dissipative eigenvalues of Maxwell's equations

Vesselin Petkov
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Abstract

Let $\Omega = \mathbb R^3 \setminus \bar{K}$, where $K$ is an open bounded domain with smooth boundary $\Gamma$. Let $V(t) = e^{tG_b},\: t \geq 0,$ be the semigroup related to Maxwell's equations in $\Omega$ with dissipative boundary condition $\nu \wedge (\nu \wedge E)+ \gamma(x) (\nu \wedge H) = 0, \gamma(x) > 0, \forall x \in \Gamma.$ We study the case when $\gamma(x) \neq 1, \: \forall x \in \Gamma,$ 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.

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Vesselin Petkov. 2022-04-25. Asymptotic of the dissipative eigenvalues of Maxwell's equations. https://arxiv.org/abs/2204.11779

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