Geodesic
Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity
Electronic journal of differential equations, Tome 2004 (2004)
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].
Classification : 35B27, 35B40, 35L05
Keywords: homogenization, asymptotic stability, wave equation 
@article{EJDE_2004__2004__a185,
     author = {Cavalcanti,  Marcelo M. and Domingos Cavalcanti,  Valeria N. and Soriano,  Juan A. and Souza,  Joel S.},
     title = {Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1053.35021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a185/}
}
TY  - JOUR
AU  - Cavalcanti,  Marcelo M.
AU  - Domingos Cavalcanti,  Valeria N.
AU  - Soriano,  Juan A.
AU  - Souza,  Joel S.
TI  - Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a185/
LA  - en
ID  - EJDE_2004__2004__a185
ER  - 
%0 Journal Article
%A Cavalcanti,  Marcelo M.
%A Domingos Cavalcanti,  Valeria N.
%A Soriano,  Juan A.
%A Souza,  Joel S.
%T Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a185/
%G en
%F EJDE_2004__2004__a185
Cavalcanti,  Marcelo M.; Domingos Cavalcanti,  Valeria N.; Soriano,  Juan A.; Souza,  Joel S. Homogenization and uniform stabilization for a nonlinear hyperbolic equation in domains with holes of small capacity. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a185/