Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity
Date
2004-04-09
Authors
Cavalcanti, Marcelo M.
Domingos Cavalcanti, V. N.
Soraino, Juan Amadeo
Souza, Joel S.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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 [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].
Description
Keywords
Homogenization, Asymptotic stability, Wave equation
Citation
Cavalcanti, 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.
Rights
Attribution 4.0 International