带强阻尼的可拉伸耦合吊桥方程指数吸引子的存在性  

Presence of exponential attractors for the equation of stretchable coupled suspension bridges with strong damping

作　　者：王雪 姜金平[1] 王思博 WANG Xue;JIANG Jinping;WANG Sibo(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2024年第2期61-67,共7页Journal of Yan'an University：Natural Science Edition

基　　金：陕西省自然科学基础研究计划项目(2018JM1042)。

摘　　要：在非线性项条件更弱的情况下,研究带强阻尼的可拉伸耦合吊桥方程的长时间动力学行为。首先,利用先验估计的方法证明解半群的有界吸收集存在;其次,利用试验函数作内积证明了方程满足加强的平坦性条件;最后,证明了带强阻尼的可拉伸耦合吊桥方程指数吸引子的存在性。研究结果进一步推广和完善了耦合吊桥方程的吸引子理论。In the case of weaker nonlinear terms,the long-term dynamic behavior of the stretchable coupled suspen⁃sion bridge equation with strong damping is studied.Firstly,the existence of bounded absorbing set of the solution semigroup is proved by a priori estimation method.Secondly,it is proved that the equation satisfies the enhanced flatness condition by using the test function as the inner product.Finally,the existence of exponential attractor for the stretchable coupled suspension bridge equation with strong damping is proved.The research results further generalize and improve the attractor theory of the coupled suspension bridge equation.

关 键 词：强阻尼 可拉伸耦合吊桥方程 指数吸引子 加强的平坦性条件 

分 类 号：O175.29[理学—数学]