PETKOV, Vesselin

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PETKOV, Vesselin
Institut de Mathématiques de Bordeaux [IMB]

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Este ítem está publicado en

Inverse Problems and Imaging. 2016-11-21, vol. 10, n° 4, p. 1111-1139

AIMS American Institute of Mathematical Sciences

Resumen en inglés

We examine the location of the eigenvalues of the generator G of a semi-group V (t) = e tG , t ≥ 0, related to the wave equation in an unbounded domain Ω ⊂ R d with dissipative boundary condition ∂ν u − γ(x)∂tu = 0 on Γ = ∂Ω. We study two cases: (A) : 0 < γ(x) < 1, ∀x ∈ Γ and (B) : 1 < γ(x), ∀x ∈ Γ. We prove that for every 0 < 1, the eigenvalues of G in the case (A) lie in the region Λ = {z ∈ C : | Re z| ≤ C Im z| 1 2 + + 1), Re z < 0}, while in the case (B) for every 0 < 1 and every N ∈ N the eigenvalues lie in Λ ∪ R N , where R N = {z ∈ C : | Im z| ≤ C N (| Re z| + 1) −N , Re z < 0}.< Leer menos

Palabras clave en inglés

dissipative boundary conditions

location of the spectrum of a generator

asymptotically disapearing solitions

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193788

Proyecto ANR

Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution - ANR-11-BS01-0019

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Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251