%0 Journal Article %T Indirect internal stabilization of weakly coupled evolution equations %+ Laboratoire de Mathématiques et Applications de Metz (LMAM) %+ Dipartimento di Matematica [Roma II] (DIPMAT) %+ Institut de Recherche Mathématique Avancée (IRMA) %A Alabau, F. %A Cannarsa, P. %A Komornik, Vilmos %< avec comité de lecture %@ 1424-3199 %J Journal of Evolution Equations %I Springer Verlag %V 2 %N 2 %P 127-150 %8 2002-05-01 %D 2002 %R 10.1007/s00028-002-8083-0 %K Asymptotic behaviour %K second order evolution equations %K stabilization %K partial differential equations %K multipier method. %Z Mathematics [math]/Optimization and Control [math.OC] %Z Mathematics [math] %Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles %X Let two second order evolution equations be coupled via the zero order terms, and suppose that thefirst one is stabilized by a distributed feedback. What will then be the effect of such a partial stabilization onthe decay of solutions at infinity? Is the behaviour of the first component sufficient to stabilize the second one?The answer given in this paper is that sufficiently smooth solutions decay polynomially at infinity, and that thisdecay rate is, in some sense, optimal. The stabilization result for abstract evolution equations is also applied tostudy the asymptotic behaviour of various systems of partial differential equations. %G English %L hal-03895223 %U https://hal-cnrs.archives-ouvertes.fr/hal-03895223 %~ CNRS %~ UNIV-METZ %~ IECN %~ IRMA %~ INSMI %~ UNIV-STRASBG %~ UNIV-LORRAINE %~ TDS-MACS %~ SITE-ALSACE