Geodesic
Asymptotic behavior for a dissipative plate equation in $\Bbb R^N$ with periodic coefficients
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Charao, Ruy Coimbra and Bisognin, Eleni and Bisognin, Vanilde and Pazoto, Ademir Fernando},
     title = {Asymptotic behavior for a dissipative plate equation in $\Bbb R^N$ with periodic coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a26/}
}
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Charao, Ruy Coimbra; Bisognin, Eleni; Bisognin, Vanilde; Pazoto, Ademir Fernando. Asymptotic behavior for a dissipative plate equation in $\Bbb R^N$ with periodic coefficients. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a26/