记忆型无阻尼抽象发展方程的强时间依赖全局吸引子

Abstract

Abstract:

In this paper, by applying the modified pullback attractors theory, asymptotic a priori estimate method and operator decomposition technique, we obtain the existence as well as regularity of strong time-dependent global attractors for the non-damping abstract evolution equations with fading memory.

Key words: Fading memory, Abstract evolution equation, Strong time-dependent global attractor, Existence, Regularity

CLC Number:

O175.27

Didi Hu,Xuan Wang. The Strong Time-Dependent Global Attractors for the Non-Damping Abstract Evolution Equations with Fading Memory[J].Acta mathematica scientia,Series A, 2019, 39(1): 81-94.

Trendmd

References 16

1	Borini S , Pata V . Uniform attractors for a strongly damped wave equations with linear memory. Asymptot Anal, 1999, 20: 263- 277
2	Coleman B D , Noll W . Foundations of linear viscoelasticity. Rev Mod Phys, 1961, 33: 239- 249 doi: 10.1103/RevModPhys.33.239
3	Conti M , Pata V , Temam R . Attractors for processes on time-dependent spaces and applications to wave equation. J Differ Equations, 2013, 255: 1254- 1277 doi: 10.1016/j.jde.2013.05.013
4	Conti M , Pata V . Asymptotic structure of the attractor for processes on time-dependent spaces. Nonlinear Anal, 2014, 19: 1- 10 doi: 10.1016/j.nonrwa.2014.02.002
5	Dafermos C M . Asymptotic stability in viscoelasticity. Arch Ration Mech Anal, 1970, 37: 297- 308 doi: 10.1007/BF00251609
6	Fabrizio M , Morro A . Mathematical Problems in Linear Viscoelasticity. Philadelphia: SAIM Stud Appl Math, 1992
7	Gatti C , Miranville A , Pata V , Zelik S V . Attractors for semilinear equations of viscoelasticity with very low dissipation. R Mountain J Math, 2008, 38: 1117- 1138 doi: 10.1216/RMJ-2008-38-4-1117
8	胡弟弟, 汪璇. 记忆型抽象发展方程时间依赖吸引子的存在性. 华东师范大学学报(自然科学版), 2018, 2018: 35- 49 doi: 10.3969/j.issn.1000-5641.2018.01.005
	Hu D D , Wang X . The existence of time-dependent attractors for abstract evolution equations with fading memory. J East China Normal Univ (Nat Sci), 2018, 2018: 35- 49 doi: 10.3969/j.issn.1000-5641.2018.01.005
9	Ma Q Z , Wang X P , Xu L . Existence and regularity of time-dependent global attractos for the nonclassical reaction-diffusion equations with lower forcing term. Bound Value Probl, 2016, 2016: 1- 11 doi: 10.1186/s13661-015-0477-3
10	Meng F J , Yang M H , Zhong C K . Attractors for wave equations with nonlinear damping on time-dependent space. Discrete Contin Dyn Syst, 2017, 21: 205- 225
11	Meng F J , Liu C C . Necessary and sufficient conditions for the existence of time-dependent global attractor and application. J Math Phys, 2017, 58: 032702 doi: 10.1063/1.4978329
12	Pata V , Zucchi A . Attractors for a damped hyperbolic equation with linear memory. Adv Math Sci Appl, 2001, 260: 505- 529
13	Temam R . Infinit Dimensional Dynamical System in Mechanichs and Physics. New York: Springer-Verlag, 1997
14	Wang X , Duan F X , Hu D D . Attractors for a class of abstract evolution equations with fading memory. Math Probl Eng, 2017, 2017: 1- 16
15	Wang X , Yang L , Zhong C K . Attractors for the nonclassical diffusion equations with fading memory. J Math Anal Appl, 2010, 362: 327- 337 doi: 10.1016/j.jmaa.2009.09.029
16	张玉宝, 汪璇. 无阻尼弱耗散抽象发展方程的强全局吸引子. 华东师范大学学报(自然科学版), 2017, 2017: 8- 19 doi: 10.3969/j.issn.1000-5641.2017.02.002
	Zhang Y B , Wang X . The strong global attractors for the non-damping weak diffusion abstract evolution equations. J East China Normal Univ (Nat Sci), 2017, 2017: 8- 19 doi: 10.3969/j.issn.1000-5641.2017.02.002

[1]	Xiaoming Peng,Xiaoxiao Zheng,Yadong Shang. Global Attractors for a Fourth Order Pseudo-Parabolic Equation with Fading Memory [J]. Acta mathematica scientia,Series A, 2019, 39(1): 114-124.
[2]	Yongzhen Yun,Youhui Su,Weimin Hu. Existence and Uniqueness of Solutions to a Class of Anti-Periodic Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator [J]. Acta mathematica scientia,Series A, 2018, 38(6): 1162-1172.
[3]	Xuan Wang, Ying Han, Chenghua Gao. Global Attractor in H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ)) for the Nonclassical Diffusion Equations with Fading Memory [J]. Acta mathematica scientia,Series A, 2018, 38(6): 1205-1223.
[4]	Xueping Luo, Mengtian Cui. Solvability of Directional Perturbed Generalized Mixed Variational Inequalities in Reflexive Banach Spaces [J]. Acta mathematica scientia,Series A, 2018, 38(6): 1144-1152.
[5]	Jun Wang,Tianlu Wang,Yanhua Wen,Xianfeng Zhou. Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay [J]. Acta mathematica scientia,Series A, 2018, 38(5): 903-910.
[6]	Zhao Jihong. Logarithmical Regularity Criteria in Terms of Pressure for the Three Dimensional Dissipative System Modeling Electro-Hydrodynamics [J]. Acta mathematica scientia,Series A, 2018, 38(3): 549-564.
[7]	Zhang Shuqin, Hu Lei. Initial Value Problem for Nonlinear Fractional Differential Equations with Variable-order Derivative and a Parameter [J]. Acta mathematica scientia,Series A, 2018, 38(2): 291-303.
[8]	Xing Chao, Ren Mengzhang, Luo Hong. The Existence of Global Weak Solutions to Thermohaline Circulation Equations [J]. Acta mathematica scientia,Series A, 2018, 38(2): 284-290.
[9]	Zhu Xincai. Existence of Constrained Minimizers for Schrödinger-Poisson Equations in R^N [J]. Acta mathematica scientia,Series A, 2018, 38(1): 61-70.
[10]	Su Xiao, Wang Shubin. Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1085-1093.
[11]	Li Qingwei, Gao Wenjie, Han Yuzhu. Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity [J]. Acta mathematica scientia,Series A, 2017, 37(5): 877-894.
[12]	Li Qin, Yang Zuodong. Infinitely Many High Energy Solutions of p-Kirchhoff-Type System with Sign-Changing Weight [J]. Acta mathematica scientia,Series A, 2017, 37(5): 869-876.
[13]	Gao Hongya, Jia Miaomiao. Local Regularity and Local Boundedness for Solutions to Obstacle Problems [J]. Acta mathematica scientia,Series A, 2017, 37(4): 706-713.
[14]	Ba Na, Zheng Lie. Partial Schauder Estimates for the Heat Equation [J]. Acta mathematica scientia,Series A, 2017, 37(2): 307-312.
[15]	Huang Decheng, Chen Shouxin. New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations [J]. Acta mathematica scientia,Series A, 2017, 37(2): 299-306.

The Strong Time-Dependent Global Attractors for the Non-Damping Abstract Evolution Equations with Fading Memory

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 16

Related Articles 15

Metrics

Comments

Recommended 10