Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 46, pp. 1-23.
Title: Asymptotic behavior for a dissipative plate equation
in $\mathbb{R}^N$ with periodic coefficients
Authors: Ruy C. Charao (Univ. Federal de Santa Catarina, Brazil)
Eleni Bisognin (Centro Univ. Franciscano, Santa Maria, Brazil)
Vanilde Bisognin (Centro Univ. Franciscano, Santa Maria, Brazil)
Ademir F. Pazoto (Univ. Federal do Rio de Janeiro, Brazil)
Abstract:
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.
Submitted June 7, 2007. Published March 29, 2008.
Math Subject Classifications: 35C20, 35B40, 35B27, 35L15.
Key Words: Asymptotic behavior; homogenization;
partial differential equations; media with periodic structure;
second-order hyperbolic equations.