Asymptotic of the dissipative eigenvalues of Maxwell’s equations
Language
en
Article de revue
This item was published in
Asymptotic Analysis. 2023-09-05, vol. 134, n° 3-4, p. 345-367
IOS Press
English Abstract
Let $\Omega = \R^3 \setminus \bar{K}$, 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 ...Read more >
Let $\Omega = \R^3 \setminus \bar{K}$, 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.Read less <
English Keywords
Dissipative boundary conditions
Dissipative eigenvalues
Weyl formula
Origin
Hal imported