Strong global attractors for non-damping weak dissipative abstract evolution equation

  • ZHANG Yu-bao ,
  • WANG Xuan
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  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received date: 2016-03-08

  Online published: 2017-03-23

Abstract

In this paper, by using the theory of semigroup, contractive function and the method of defining functionals, the existence of the global attractors for nondamping weak dissipative abstract evolution equations with strong solutions in the space V2θ×Vθ×Lμ2(R+;V2θ was obtained when the nonlinear term satisfies the weaker dissipative condition.

Cite this article

ZHANG Yu-bao , WANG Xuan . Strong global attractors for non-damping weak dissipative abstract evolution equation[J]. Journal of East China Normal University(Natural Science), 2017 , 2017(2) : 8 -19 . DOI: 10.3969/j.issn.1000-5641.2017.02.002

References

[1] COLEMAN B D, NOLL W. Foundations of linear viscoelasticity[J]. Reviews of Modern Physics, 1961, 33(2):239-249.
[2] DAFERMOS C M. Asymptotic stability in viscoelasticity[J]. Archive for Rational Mechanics and Analysis, 1970, 37(4):297-308.
[3] FABRIZIO M, MORRO A. Mathematical Problems in Linear Viscoelasticity[M]. Pennsylvania:Society for Industrial and Applied Mathematics, 1992.
[4] GIORGI C, RIVERA J M, PATA V. Global attractors for a semilinear hyperbolic equations in viscoelasticity[J]. J Math Anal Appl, 2001, 260(1):83-99.
[5] PATA V, ZUCCHI A. Attractors for a damped hyperbolic equation with linear memory[J]. Adv Math Sci Appl, 2001, 11(2):505-529.
[6] MA Q Z, ZHONG C K. Exitence of strong global attractors for hyperbolic equation with linear memory[J]. Applied Mathematics and Computation, 2004, 157(3):745-758.
[7] SUN C Y, CAO D M, DUAN J Q. Non-autonomous wave dynamics with memory-asymptotic regularity and uniform attractors[J]. Discrete & Continuous Dynamical Systems, 2008, 9(3-4):743-761.
[8] TEMAM R. Infinite Dimensional Dynamical System in Mechanics and Physics[M]. 2nd ed. New York:SpringVerlag, 1997.
[9] 马巧珍, 孙春友, 钟承奎. 非线性梁方程强全局吸引子的存在性[J].数学物理学报, 2007, 27(5): 941-948.
[10] ANGUIANO M, MARIN-RUBIO P, REAL J. Regularity results and exponential growth for pullback attractors of a non-autonomous reaction-diffusion model with dynamical boundary conditions[J]. Nonlinear Analysis Real World Applications, 2014, 20(1):112-125.
[11] 汪璇, 段奋霞, 马群, 等. 带衰退记忆的经典反应扩散方程的强全局吸引子[J]. 数学年刊,(中文版),2015, 35(3): 265-276.
[12] MA Q Z, XU L. Random attractors for the extensible suspension bridge equation with white noise[J]. Computers & Mathematics with Applications, 2015, 70(12):2895-2903.
[13] 王春梅, 汪璇, 钟承奎. 弱耗散抽象发展方程全局吸引子的存在性[J].纯粹数学与应用数学, 2012, 28(3): 401-411.
[14] ZHONG C K, YANG M H, SUN C Y. The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations[J]. Journal of Differential Equations, 2006, 223(2):367-399.
[15] WANG X, YANG L, ZHONG C K. Attractors for the nonclassical diffusion equations with fading memory[J]. Journal of Mathematical Analysis & Applications, 2010, 362(2):327-337.
[16] SUN C Y, CAO D M, DUAN J Q. Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity[J]. Nonlinearity, 2006, 19(11):2645-2665.
[17] ROBINSON J C. Infinite-dimensional Dynamical Systems:An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors[M]. Cambridge:Cambridge University Press, 2001.

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