非自治记忆型强阻尼波方程的拉回指数吸引子  

Pullback exponential attractor of the non-autonomous memory strong damping wave equation

作　　者：任丽宇 姜金平[1] 刘生清 罗轩怡 REN Liyu;JIANG Jinping;LIU Shengqing;LUO Xuanyi(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）》2023年第2期91-98,共8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);陕西省大学生创新创业计划训练项目(S202010719058)。

摘　　要：研究了非自治记忆型强阻尼波方程的拉回指数吸引子存在问题。利用耗散过程的一致挤压性质,对拉回吸引子的每个集合延伸扩展,使得它的一致有界吸收集有有限分形维数,进而利用分解方法验证过程的ω-渐近紧性,并且拉回指数吸引子以指数速率拉回吸引相空间中的每个子集,最后证明了拉回指数吸引子的存在性。The problem of pullback exponential attractors of non-autonomous memory strong damping wave equation was studied.Using the consistent extrusion property of the dissipation process,each set of pullback attractors was extended and expanded to give its uniform bounded absorption set a finite fractal dimension before the decomposition method was used to verify the asymptotic tightness of the process.The exponential rate pulled back each subset of the attraction phase space,which finally proved the existence of the pullback exponential attractor.

关 键 词：波方程 拉回指数吸引子 记忆型 强阻尼 

分 类 号：O175.2[理学—数学]