Asymptotic of the dissipative eigenvalues of Maxwell's equations

2022/04/25 by Vesselin Petkov, Petkov, Vesselin
Computer Science · Mathematics · #35P20 #35P25 #35Q61 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2204.11779

openalex publication_date 2022/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω= \mathbb R³ ∖ K, where K is an open bounded domain with smooth boundary Γ. Let V(t) = e^tG_b, t ≥ 0, be the semigroup related to Maxwell's equations in Ω with dissipative boundary condition ν\wedge (ν\wedge E)+ γ(x) (ν\wedge 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 G_b in a polynomial neighbourhood of the negative real axis.

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