Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
Eleni Bisognin, Vanilde Bisognin, Ademir Fernando Pazoto, Ruy Coimbra Charão · DOAJ (DOAJ: Directory of Open Access Journals) · 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 $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.