Abstract
We study the large time behavior of the solutions of ∂ 2 t — Δ + 2a(x)∂ t on a compact Riemannian manifold M with boundary (a(x)≥ 0). We give a formula for the exponential decay rate in term of the spectrum and of the average of a(x) on the geodesics of M.
Résumé
On étudie le comportement pour t → + ∞ des solutions d’équations d’ondes du type ∂ 2 t — Δ + 2a(x) ∂ t , sur une variété compacte riemannienne M à bord, avec a(x) ≥ 0. On calcule en particulier le taux de décroissance exponentielle en fonction du spectre et des moyennes de a(x) sur les géodésiques de M.
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© 1996 Springer Science+Business Media Dordrecht
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Lebeau, G. (1996). Equation des Ondes Amorties. In: de Monvel, A.B., Marchenko, V. (eds) Algebraic and Geometric Methods in Mathematical Physics. Mathematical Physics Studies, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0693-3_4
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DOI: https://doi.org/10.1007/978-94-017-0693-3_4
Publisher Name: Springer, Dordrecht
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