Exponential decay for damped Klein–Gordon equations on asymptotically cylindrical and conic manifolds
[Décroissance exponentielle pour les équations de Klein–Gordon amorties sur des variétés asymptotiquement cylindriques et coniques]
Wang, Ruoyu P. T.1
1 Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, Illinois 60208 (USA)
Annales de l'Institut Fourier, Online first, 44 p.

Nous étudions la décroissance de l’énergie globale pour l’équation de Klein–Gordon amortie sur des variétés non compactes avec un nombre fini des bouts cylindriques et subconiques jusqu’à une perturbation bornée. Nous prouvons que sous la condition de contrôle géométrique, la décroissance est exponentielle, et que sous la condition de contrôle de réseau plus faible, la décroissance est logarithmique, en développant l’estimation globale de Carleman avec des poids multiples.

We study the decay of the global energy for the damped Klein–Gordon equation on non-compact manifolds with finitely many cylindrical and subconic ends up to bounded perturbation. We prove that under the Geometric Control Condition, the decay is exponential, and that under the weaker Network Control Condition, the decay is logarithmic, by developing the global Carleman estimate with multiple weights.

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Révisé le :
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DOI : 10.5802/aif.3623
Classification : 35L05
Keywords: Damped waves, damped Klein–Gordon, exponential decay, non-compact manifolds, Carleman estimates.
Mot clés : Ondes amorties, Klein–Gordon amorti, décroissance exponentielle, variétés non-compactes, estimations de Carleman.
Wang, Ruoyu P. T. 1

1 Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, Illinois 60208 (USA) 
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Wang, Ruoyu P. T. Exponential decay for damped Klein–Gordon equations on asymptotically cylindrical and conic manifolds. Annales de l'Institut Fourier, Online first, 44 p.

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