Cavalcanti, Marcelo M.Domingos Cavalcanti, V. N.Soraino, Juan AmadeoSouza, Joel S.2021-04-192021-04-192004-04-09Cavalcanti, M. M., Domingos Cavalcanti, V. N., Soriano, J. A., & Souza, J. S. (2004). Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity. <i>Electronic Journal of Differential Equations, 2004</i>(55), pp. 1-19.1072-6691https://hdl.handle.net/10877/13392In this article we study the homogenization and uniform decay of the nonlinear hyperbolic equation ∂ttuɛ - Δuɛ + F(x, t, ∂tuɛ, ∇uɛ) = 0 in Ωɛ x (0, +∞) where Ωɛ is a domain containing holes with small capacity (i.e. the holes are smaller than a critical size). The homogenization's proofs are based on the abstract framework introduced by Cioranescu and Murat [8] for the study of homogenization of elliptic problems. Moreover, uniform decay rates are obtained by considering the perturbed energy method developed by Haraux and Zuazua [10].Text19 pages1 file (.pdf)enAttribution 4.0 InternationalHomogenizationAsymptotic stabilityWave equationArticle