Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 55, pp. 1-19.

Title: Homogenization and uniform stabilization for a nonlinear
       hyperbolic equation in domains with holes of small capacity

Authors: Marcelo M. Cavalcanti (Univ. Estadual de Maringa, Brasil)
         Valeria N. Domingos Cavalcanti (Univ. Estadual de Maringa, Brasil)
         Juan A. Soriano (Univ. Estadual de Maringa, Brasil)
	 Joel S. Souza (Univ. Federal de Santa Catarina, Brasil)

Abstract: 
 In this article we study the homogenization and
 uniform decay of the nonlinear hyperbolic equation
 $$
 \partial_{tt} u_{\varepsilon} -\Delta u_{\varepsilon}
 +F(x,t,\partial_t u_{\varepsilon},\nabla u_{\varepsilon})=0
 \quad\hbox{in }\Omega_{\varepsilon}\times(0,+\infty)
 $$
 where $\Omega_{\varepsilon}$  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].
  
Submitted September 23, 2003. Published April 9, 2004.
Math Subject Classifications: 35B27, 35B40, 35L05
Key Words: Homogenization; asymptotic stability; wave equation.