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

作　　者：刘润杰 徐玲 LIU Runjie;XU Ling(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《大连理工大学学报》2025年第3期321-330,共10页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11961059,12101502);高校教师创新基金资助项目(2023B-062).

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.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.

关 键 词：板方程 Kirchhoff型 非局部弱阻尼 反阻尼 全局吸引子 

分 类 号：O175.8[理学—数学]