Affiliation:
1. Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France
Abstract
Let Ω = R 3 ∖ K ¯, where K is an open bounded domain with smooth boundary Γ. Let V ( t ) = e t G b , 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 G b in a polynomial neighbourhood of the negative real axis.
Reference12 articles.
1. Weyl formula for the negative dissipative eigenvalues of Maxwell’s equations;Colombini;Archiv der Mathemtik,2018
2. Spectral problems for non elliptic symmetric systems with dissipative boundary conditions;Colombini;J. Funct. Anal.,2014
3. Eigenvalues for Maxwell’s equations with dissipative boundary conditions;Colombini;Asymptotic Analysis,2016
4. M. Dimassi and J. Sjöstrand, Spectral Asymptotics in Semi-Classical Limits, London Mathematical Society, Lecture Notes Series, Vol. 268, Cambridge University Press, 1999.
5. A. Kirsch and F. Hettlich, The Mathematical Theory of Time-Harmonic Maxwell’s Equations, Applied Mathematical Sciences, Vol. 190, Springer, Switzerland, 2015.