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中文摘要：
对具有结构阻尼和外阻尼的更一般的非线性粘弹性梁方程,在夹钳边界条件和初始条件下,利用Galerkin方法,并结合先验估计,证明了系统的整体强解的存在唯一性;通过先验估计,并结合一些不等式,证明了系统的有界吸收集的存在性;利用已知的验证紧性的方法,证明了系统所确定的半群的紧致性,从而证明了非线性粘弹性梁方程系统的强的整体吸引子的存在性.
英文摘要：
A generalized nonlinear equation of elastic beam with both structural damping and external damping was considered.By using Galerkin method combined with prior estimates,the existence and uniqueness of global strong solutions were proved under hinged boundary conditions and initial conditions.Through the prior estimates and some inequality,the existence of the bounded absorbing set of above-mentioned system was obtained.By taking the proposed method for compact property verification,the compactness of group determined by the above system was proved,and the existence of the strong global attractor of beam equation was proved.
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