Geodesic
Asymptotic behavior for a dissipative plate equation in \(\mathbb R^N\) with periodic coefficients
Electronic journal of differential equations, Tome 2008 (2008)
In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $\mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $t\to \infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
Classification : 35C20, 35B40, 35B27, 35L15
Keywords: asymptotic behavior, homogenization, partial differential equations, media with periodic structure, second-order hyperbolic equations 
@article{EJDE_2008__2008__a26,
     author = {Charao,  Ruy Coimbra and Bisognin,  Eleni and Bisognin,  Vanilde and Pazoto,  Ademir Fernando},
     title = {Asymptotic behavior for a dissipative plate equation in \(\mathbb {R^N\)} with periodic coefficients},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1170.35319},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a26/}
}
TY  - JOUR
AU  - Charao,  Ruy Coimbra
AU  - Bisognin,  Eleni
AU  - Bisognin,  Vanilde
AU  - Pazoto,  Ademir Fernando
TI  - Asymptotic behavior for a dissipative plate equation in \(\mathbb R^N\) with periodic coefficients
JO  - Electronic journal of differential equations
PY  - 2008
VL  - 2008
UR  - http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a26/
LA  - en
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%A Charao,  Ruy Coimbra
%A Bisognin,  Eleni
%A Bisognin,  Vanilde
%A Pazoto,  Ademir Fernando
%T Asymptotic behavior for a dissipative plate equation in \(\mathbb R^N\) with periodic coefficients
%J Electronic journal of differential equations
%D 2008
%V 2008
%U http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a26/
%G en
%F EJDE_2008__2008__a26
Charao,  Ruy Coimbra; Bisognin,  Eleni; Bisognin,  Vanilde; Pazoto,  Ademir Fernando. Asymptotic behavior for a dissipative plate equation in \(\mathbb R^N\) with periodic coefficients. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a26/