具有非局部弱阻尼和反阻尼的板方程全局吸引子

Global attractors for plate equations with nonlocal weak damping and anti-damping

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 damping  anti-damping  global attractors

中文摘要:

      当非线性项的增长指数为临界情形时，证明了具有非局部弱阻尼和反阻尼的Kirchhoff型板方程的全局吸引子的存在性．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:

      The existence of global attractors for the Kirchhoff-type plate equation with nonlocal weak damping and anti-damping is proved when the growth exponent of the nonlinearity is up to the critical cases. Firstly, the global well-posedness of solution is proved by the well-posedness theory for the development equation of m-accretive 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 discussed equation is obtained.