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Existence and decay of solutions of a coupled system of plates. (English) Zbl 1116.35082
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