Sanguino Bejarano, S. R. W.; Milla Miranda, Manuel Existence and decay of solutions of a coupled system of plates. (English) Zbl 1116.35082 Panam. Math. J. 16, No. 3, 1-18 (2006). Summary: We study the mixed problem with boundary dissipation conditions for the following system: \[ \begin{aligned} u''+\ell v''+\alpha \Delta^2u-\Delta u=0\quad & \text{in }\Omega\times]0,\infty[\\ \ell u''+\gamma v''+\delta\Delta^2v-\beta \Delta v=0\quad & \text{in } \Omega\times]0,\infty[\end{aligned} \] where \(\Omega\) is a smooth bounded domain of \(\mathbb{R}^2\). Existence and exponential decay of solutions are obtained. By the Galerkin method we find the existence. MSC: 35L55 Higher-order hyperbolic systems 74K20 Plates 35L75 Higher-order nonlinear hyperbolic equations 35L35 Initial-boundary value problems for higher-order hyperbolic equations Keywords:boundary dissipation conditions; Galerkin method PDFBibTeX XMLCite \textit{S. R. W. Sanguino Bejarano} and \textit{M. Milla Miranda}, Panam. Math. J. 16, No. 3, 1--18 (2006; Zbl 1116.35082)