In this paper, we consider the nonlinearly damped nonlinear coupled wave and Petrovsky system$$\begin{aligned}&u'' + \Delta ^{2} u+ av + g_{1}(u')=f_{1}(u,v), \\&v'' - \Delta v+ au + g_{2}(v')=f_{2}(u,v). \end{aligned}$$We prove the global existence of solutions by means of the stable set method in \(H_{0}^{2}(\Omega )\times H^1_0(\Omega )\) combined with the Faedo–Galerkin procedure. Furthermore, we establish a more general energy decay of solutions when the nonlinear dissipative terms \(g_{1},g_{2}\) do not necessarily have a polynomial growth near the origin.

中文翻译：

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具有非线性耗散和源项的波和彼得罗夫斯基耦合系统解的整体存在性和能量衰减

在本文中，我们考虑了非线性阻尼非线性耦合波和Petrovsky系统$$ \ begin {aligned}＆u''+ \ Delta ^ {2} u + av + g_ {1}（u'）= f_ {1}（u ，v），\\＆v''-\ Delta v + au + g_ {2}（v'）= f_ {2}（u，v）。\ {端对齐} $$我们通过在稳定集方法来证明解决方案的整体存在（H ^ 1_0（\欧米茄）\ H_ {0} ^ {2}（\欧米茄）\次）\与组合Faedo-Galerkin程序。此外，当非线性耗散项\（g_ {1}，g_ {2} \）不一定在原点附近具有多项式增长时，我们建立了更通用的解能量衰减。