2015/06/08 by Ferruccio Colombini, Colombini, Ferruccio, Vesselin Petkov +3
Mathematics · Physics and Astronomy · #35P20 (Primary) #35Q61 (Secondary) #47A40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35P20 #msc:35Q61 #msc:47A40
paper · pdf · doi:10.48550/arxiv.1506.02555
to appear in Asymptotic Analysis
arxiv created 2016/08/04 · arxiv updated 2016/08/05
Let V(t) = etGb, t ≥ 0, be the semigroup generated by Maxwell's equations in an exterior domain Ω⊂ \mathbb R3 with dissipative boundary condition Etan- γ(x) (ν\wedge Btan) = 0, γ(x) > 0, ∀ x ∈ Γ= ∂ Ω. We prove that if γ(x) is nowhere equal to 1, then for every 0 < ε≪ 1 and every N ∈ \mathbb N the eigenvalues of Gb lie in the region Λε ∪ \mathcal RN, where Λε = \ z ∈ \mathbb C: |\Re z | ≤ Cε (|\Im z|(1)/(2) + ε + 1), \Re z < 0\, \mathcal RN = \z ∈ \mathbb C: |\Im z| ≤ CN (|\Re z| + 1)-N, \Re z < 0\.