English

Asymptotic of the dissipative eigenvalues of Maxwell's equations

Analysis of PDEs 2023-03-14 v3 Mathematical Physics math.MP

Abstract

Let Ω=R3Kˉ\Omega = \mathbb R^3 \setminus \bar{K}, where KK is an open bounded domain with smooth boundary Γ\Gamma. Let V(t)=etGb,t0,V(t) = e^{tG_b},\: t \geq 0, be the semigroup related to Maxwell's equations in Ω\Omega with dissipative boundary condition ν(νE)+γ(x)(νH)=0,γ(x)>0,xΓ.\nu \wedge (\nu \wedge E)+ \gamma(x) (\nu \wedge H) = 0, \gamma(x) > 0, \forall x \in \Gamma. We study the case when γ(x)1,xΓ,\gamma(x) \neq 1, \: \forall x \in \Gamma, and we establish a Weyl formula for the counting function of the eigenvalues of GbG_b in a polynomial neighbourhood of the negative real axis.

Keywords

Cite

@article{arxiv.2204.11779,
  title  = {Asymptotic of the dissipative eigenvalues of Maxwell's equations},
  author = {Vesselin Petkov},
  journal= {arXiv preprint arXiv:2204.11779},
  year   = {2023}
}

Comments

Several misprints have been corrected