文章摘要
具有非局部弱阻尼和反阻尼的 Kirchhoff 型板方程全局吸引子的存在性
Existence of Global Attractors for Kirchhoff Plate Equations with Nonlocal Weak Damping and Anti-damping
投稿时间:2023-12-28  修订日期:2024-01-25
DOI:
中文关键词: 板方程  Kirchhoff 型  非局部弱阻尼  反阻尼  全局吸引子
英文关键词: plate equations  Kirchhoff-type  nonlocal weak damp  anti-damping  global attractors
基金项目:国家自然科学基金项目(11961059, 1210502); 高校教师创新基金项目~(2023B-062)
作者单位
刘润杰 西北师范大学 
徐玲* 西北师范大学 
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中文摘要:
      本文考虑非线性项的增长指数为临界情形时, 具有非局部弱阻尼和反阻尼的 Kirchhoff 型板方程的全局吸引子. 首先运用带有局部 Lipschitz 扰动的 m-增生算子发展方程的适定性理论证明了解的全局适定性; 其次, 通过构造一个新的 Gronwall 不等式证明了该系统的耗散性; 最后运用压缩函数法讨论了该方程的渐近光滑性, 进而得到所讨论方程全局吸引子的存在性.
英文摘要:
      In this paper, we consider the global attractors of the Kirchhoff plate equation with nonlocal weak damping and anti-damping when the growth exponent of the nonlinearity is up to the critical cases. Firstly, the global well-posedness is proved by the theory of the development equation of monotone operator with local Lipschitz perturbation. Secondly, the dissipative property of the system is proved by constructing a new Gronwall inequality. Finally, the asymptotic smoothness of the equation is discussed by using the compression function method, and then the existence of the global attractor of the equation is obtained.
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