We study asymptotic synchronization at the level of global attractors in a class of coupled second order in time models which arises in dissipative wave and elastic structure dynamics. Under some conditions we prove that this synchronization arises in the infinite coupling intensity limit and show that for identical subsystems this phenomenon appears for finite intensities. Our argument involves a method based on "compensated" compactness and quasi-stability estimates. As an application we consider the nonlinear Kirchhoff, Karman and Berger plate models with different types of boundary conditions. Our results can be also applied to the nonlinear wave equations in an arbitrary dimension. We consider synchronization in sine-Gordon type models which describes distributed Josephson junctions.

中文翻译：

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时间无限维模型中耦合二阶同步

我们研究了在耗散波和弹性结构动力学中出现的时间模型中一类耦合二阶全局吸引子水平的渐近同步。在某些条件下，我们证明了这种同步出现在无限耦合强度限制中，并表明对于相同的子系统，这种现象出现在有限强度下。我们的论点涉及一种基于“补偿”紧凑性和准稳定性估计的方法。作为一个应用，我们考虑具有不同类型边界条件的非线性 Kirchhoff、Karman 和 Berger 板模型。我们的结果也可以应用于任意维度的非线性波动方程。我们考虑描述分布式约瑟夫森结的正弦-戈登型模型中的同步。