Asymptotic of the dissipative eigenvalues of Maxwell’s equations

Article type: Research Article

Authors: Petkov, Vesselin^{; *}

Affiliations: Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France

Correspondence: [*] Corresponding author. E-mail: petkov@math.u-bordeaux.fr.

Abstract: Let Ω=R3∖K¯, where K is an open bounded domain with smooth boundary Γ. Let V(t)=etGb, t⩾0, be the semigroup related to Maxwell’s equations in Ω with dissipative boundary condition ν∧(ν∧E)+γ(x)(ν∧H)=0, γ(x)>0, ∀x∈Γ. We study the case when γ(x)≠1, ∀x∈Γ, and we establish a Weyl formula for the counting function of the eigenvalues of Gb in a polynomial neighbourhood of the negative real axis.

Keywords: Dissipative boundary conditions, dissipative eigenvalues, Weyl formula

DOI: 10.3233/ASY-231837

Journal: Asymptotic Analysis, vol. 134, no. 3-4, pp. 345-367, 2023