HAL CCSD Indirect internal stabilization of weakly coupled evolution equations Alabau, F. Cannarsa, P. Komornik, Vilmos Laboratoire de Mathématiques et Applications de Metz (LMAM) ; Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS) Dipartimento di Matematica [Roma II] (DIPMAT) ; Università degli Studi di Roma Tor Vergata [Roma] Institut de Recherche Mathématique Avancée (IRMA) ; Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS) International audience ISSN: 1424-3199 EISSN: 1424-3202 Journal of Evolution Equations Springer Verlag hal-03895223 https://cnrs.hal.science/hal-03895223 https://cnrs.hal.science/hal-03895223 Journal of Evolution Equations, 2002, 2 (2), pp.127-150. &#x27E8;10.1007/s00028-002-8083-0&#x27E9; DOI: 10.1007/s00028-002-8083-0 info:eu-repo/semantics/altIdentifier/doi/10.1007/s00028-002-8083-0 en Asymptotic behaviour second order evolution equations stabilization partial differential equations multipier method. [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] [MATH]Mathematics [math] [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] info:eu-repo/semantics/article Journal articles 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. 2002-05-01