秦玉明,董小磊
Qin Yuming,Dong Xiaolei

• 1:东华大学理学院

摘要(Abstract)：

主要研究二维具有记忆项的非自治热弹板的一致吸引子及解的存在性和解衰减性问题.首先利用发展方程中的半群理论证明了解的存在性;接着通过构造李雅普诺夫泛函证明了该系统的衰减性;最后借助构造压缩函数验证了轨道紧性,从而得到了一致吸引子的存在性.
In this paper,we aim to investigate the existence of uniform attractors and global solution and the decay of the global solution for a 2 Dnon-autonomous linear thermoelastic plate with memory effects.For this end,we need to firstly establish the existence of global solutions by employing the method of semigroup theory.Then we can get the decay of this system by making use of the method of Lyapunov functional.At last,we also can obtain the orbit compactness by the method of contraction function.we thus prove the existence of attractors.

关键词(KeyWords)： 热弹板;吸引子;整体解;衰减性;压缩函数
thermoelastic;attractor;global solution;decay;contraction function

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11671075)

作者(Author): 秦玉明,董小磊
Qin Yuming,Dong Xiaolei

DOI: 10.16366/j.cnki.1000-2367.2018.02.001

参考文献(References)：

• [1]Zelati M C,Dell′oro F,Pata V.Energy decay of type III linear thermoelastic plates with memory[J].J Math Anal Appl,2013,401(1):357-366.
• [2]Giorgi C,Pata V.Stability of abstract linear thermoelastic systemswith memory[J].Mathematical Models and Methods in Applied Sciences,2008,11(11):627-644.
• [3]Grasselli M,Mu1oz Rivera J E,Pata V.On the energy decay of the linear thermoelastic plate with memory[J].J Math Anal Appl,2005,309:1-14.
• [4]Dell′oro F,Mu1oz J E,Pata V.Stability properties of an abstract system with applications to linear thermoelastic plates[J].J Evol Equ,2013,13:777-794.
• [5]Grasselli M,Pata V.Uniform attractors of nonautonomous systems with memory,in“Evolution Equations,Semigroups and Functional Analysis”[M].Boston:Birkhauser,2002.
• [6]Fabrizio M,Lazzari B,Mu1oz Rivera J E.Asymptotic behaviour of a thermoelastic plate of weakly hyperbolic type[J].Differential Integral Equations,2000,13:1347-1370.
• [7]Grasselli M,Squassina M.Exponential stability and singular limit for a linear thermoelastic plate with memory effects[J].Advances in Mathematical Sciences and Application,2006,16(1):15-31.
• [8]Qin Y.Integral and Discrete Inequalities and Their Applications:Volume I:Nonlinear Inequalities[M].Basel:Birkhauser,2016.
• [9]Qin Y.Integral and Discrete Inequalities and Their Applications:Volume II:Nonlinear Inequalities[M].Basel:Birkhauser,2016.
• [10]Qin Y.Analytic Inequalities and Their Applications in PDEs[M].Basel:Birkhauser,2017.
• [11]Zheng S.Nonlinear Evolution Equations[M].Florida:CRC Press,2004.
• [12]Qin Y,Wei T.Global Existence,Asymptotic Behavior and Uniform Attractors for Non-autonomous Thermoelastic Systems[J].Acta Mathematicae Applicatae Sinica English,2016,32(4):1015-1034.
• [13]Chepyzhov V V,Vishik M I.Attractors for equations of mathematical physics[M].Rhode Island:American Mathematical Society,2002.
• [14]Temam R.Infinite dimensional dynamical systems in mechanics,physics[M].New York:Springer,1997.
• [15]Chueshov I,Lasiecka I.Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping[J].Memoirs of the American Mathematical Society,2008,195(12):1-83.
• [16]Chepyzhov V V,Pata V,Vishik M I.Averaging of 2 DNavier-Stokes equations with singularly oscillating external forces[J].Nonlinearity,2009,22:351-370.
• [17]Qin Y,Feng B,Zhang M.Uniform attractors for a non-autonomous viscoelastic equation with history[J].Nonlinear Analysis,2014,101:1-5.
• [18]Sun C,Cao D,Duan J.Uniform attractor for non-autonomous wave equations with nonlinear damping[J].SIAM J Appl Dyn Syst,2007,6:293-318.
• [19]Yang L.Uniform attractor for non-autonomous plate equation with a localized damping,critical nonlinearity[J].J Math Anal Appl,2008,338:1243-1254.