具变系数和弱阻尼的非局部高阶波方程的长时间动力学行为-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Long-time Dynamic Behavior of Nonlocal Higher-Order Wave Equations with Variable Coefficients and Weak Damping

作者:: 吕鹏辉1; 余莎莎2; 林国广3; 1.苏州大学应用技术学院，江苏苏州 215325；2.苏州工业园区星洋学校，江苏苏州 215127；3.云南大学数学与统计学院，云南昆明 650500

Author(s):: Lü Penghui1; YU Shasha2; LIN Guoguang3; 1.Applied Technology College of Soochow University,Suzhou 215325,China;2.Suzhou Industrial Park Xingyang School,Suzhou 215127,China;3.School of Mathematics and Statistics,Yunnan University,Kunming 650500,China

Keywords:: nonlocal higher-order wave equation; global solution; weak damping with variable coefficient; family of global attractors

摘要:: 研究具变系数和弱阻尼的非局部高阶波方程的渐近行为。通过合理的先验估计及经典Galerkin方法，证明方程整体解的存在唯一性；根据先验估计引理，得到有界吸收集。结果表明，当变系数a(x)≥a00>0时，该类方程存在整体吸引子族。

Abstract:: The asymptotic behavior of nonlocal higher-order wave equation with variable coefficients and weak damping was studied.The existence and uniqueness of global solution of the equation were proved by reasonable prior estimation and classical Galerkin method. Then the bounded absorption set was obtained according to the prior estimation lemma.Finally,when the variable coefficient a(x)≥a00>0,the family of global attractors of the equation was obtained.