Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity
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In 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  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 .
CitationCavalcanti, 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. Electronic Journal of Differential Equations, 2004(55), pp. 1-19.
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