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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.14 no.2 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000200008 

CUBO A Mathematical Journal Vol.14, No02, (153-173). June 2012

Texto completo disponíble en formato PDF

Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle

 

Yavar Kian

Centre de Physique Theorique CNRS-Luminy, Case 907, 13288 Marseille, France. email: Yavar.Kiand@cpt.univ-mrs.fr


ABSTRACT

Consider the mixed problem with Dirichelet condition associated to the wave equation , where the scalar metric periodic in t and uniformly equal to 1 outside a compact set in x, on a T-periodic domain. Let be the associated propagator. Assuming that the perturbations are non-trapping, we prove the meromorphic continuation of the cut-off resolvent of the Floquet operator and we establish sufficient conditions for local energy decay.

Keywords and Phrases: time-dependent perturbation, moving obstacle, local energy decay, wave equation.


RESUMEN

Considere el problema mixto con condiciones de Dirichlet asociadas a la ecuación de onda , donde la metrica escalar a(t; x) es T-periódica en t y uniformemente igual a 1 fuera de un conjunto compacto en x, sobre un dominio T-periodico. Sea U(t,0) el propagador asociado. Asumiendo que las perturbaciones son non-trapping, probamos la continuacióon meromorfa de la resolvente de corte del operador de Floquet U(T, 0) y establecemos condiciones suficientes para la decadencia local de energía.

2010 AMS Mathematics Subject Classification: 35B40, 35L15 .


 

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Received: November 2011.Revised: November 2011.