| 具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子 |
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| 引用本文： | 王旦霞,王银珠.具有结构阻尼和外阻尼的非线性梁方程的强全局吸引子[J].中北大学学报,2012(1):4-8,13. |
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| 作者姓名： | 王旦霞 王银珠 |
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| 作者单位： | 太原理工大学数学学院;太原科技大学应用科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11172194);山西省自然科学基金资助项目(2010011008);山西省青年科学基金资助项目(2011021002-2) |
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| 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.
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| 关 键 词： | 结构阻尼 外阻尼 非线性梁 强整体吸引子 |
Strong Global Attractor for the Nonlinear Beam Equations with Structural Damping and External Damping |
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| WANG Dan-xia,WANG Yin-zhu.Strong Global Attractor for the Nonlinear Beam Equations with Structural Damping and External Damping[J].Journal of North University of China,2012(1):4-8,13. |
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| Authors: | WANG Dan-xia WANG Yin-zhu |
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| Affiliation: | 1,2(1.College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;2.School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China) |
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| Abstract: | 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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| Keywords: | structural damping external damping nonlinear beam strong global attractor |
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