EIGENVALUES FOR MAXWELL'S EQUATIONS WITH DISSIPATIVE BOUNDARY CONDITIONS

Ferruccio Colombini (1) , Vesselin Petkov (2) , Jeffery Rauch (3)

1 Dipartimento di Matematica
2 IMB - Institut de Mathématiques de Bordeaux
3 Department of Mathematics - University of Michigan

Let V (t) = e tG b , t ≥ 0, be the semigroup generated by Maxwell's equations in an exterior domain Ω ⊂ R 3 with dissipative boundary condition Etan − γ(x)(ν ∧ Btan) = 0, γ(x) > 0, ∀x ∈ Γ = ∂Ω. We prove that if γ(x) is nowhere equal to 1, then for every 0 < 1 and every N ∈ N the eigenvalues of G b lie in the region Λ ∪ R N , where Λ = {z ∈ C : | Re z| ≤ C Im z| 1 2 + + 1), Re z < 0}, R N = {z ∈ C : | Im z| ≤ C N (| Re z| + 1) −N , Re z < 0}.

Mots clés: Maxwell's equations; dissipative boundary conditions; asymptotically disappearing solutions

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Ferruccio Colombini, Vesselin Petkov, Jeffery Rauch. EIGENVALUES FOR MAXWELL'S EQUATIONS WITH DISSIPATIVE BOUNDARY CONDITIONS. Asymptotic Analysis, 2016, 99 (1-2). ⟨hal-01256467v2⟩