Let $V(t) = e^tG_b,: t geq 0,$ be the semigroup generated by Maxwell's equations in an exterior domain $Omega subset mathbb R^3$ with dissipative boundary condition $E_tan- gamma(x) ( u wedge B_tan) = 0, gamma(x) > 0, orall x in Gamma = partial Omega.$ We study the case when $Omega = \x in mathbb R^3:: |x| > 1$ and $gamma eq 1$ is a constant. We establish a Weyl formula for the counting function of the negative real eigenvalues of $G_b.$
Weyl formula for the negative dissipative eigenvalues of Maxwell's equations
COLOMBINI, FERRUCCIO;
2018-01-01
Abstract
Let $V(t) = e^tG_b,: t geq 0,$ be the semigroup generated by Maxwell's equations in an exterior domain $Omega subset mathbb R^3$ with dissipative boundary condition $E_tan- gamma(x) ( u wedge B_tan) = 0, gamma(x) > 0, orall x in Gamma = partial Omega.$ We study the case when $Omega = \x in mathbb R^3:: |x| > 1$ and $gamma eq 1$ is a constant. We establish a Weyl formula for the counting function of the negative real eigenvalues of $G_b.$File in questo prodotto:
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