May  2008, 9(3&4, May): 743-761. doi: 10.3934/dcdsb.2008.9.743

Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor

1. 

Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, China

2. 

Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080

3. 

Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received  January 2007 Revised  April 2007 Published  February 2008

The dynamical behavior of non-autonomous strongly damped wave-type evolutionary equations with linear memory, critical nonlinearity, and time-dependent external forcing is investigated. The time-dependent external forcing is assumed to be only translation-bounded, instead of translation-compact. First, the asymptotic regularity of solutions is proved, and then the existence of the compact uniform attractor together with its structure and regularity is obtained.
Citation: Chunyou Sun, Daomin Cao, Jinqiao Duan. Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 743-761. doi: 10.3934/dcdsb.2008.9.743
[1]

Shengfan Zhou, Linshan Wang. Kernel sections for damped non-autonomous wave equations with critical exponent. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 399-412. doi: 10.3934/dcds.2003.9.399

[2]

Zhaojuan Wang, Shengfan Zhou. Random attractor for stochastic non-autonomous damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 545-573. doi: 10.3934/dcds.2017022

[3]

Xiaolin Jia, Caidi Zhao, Juan Cao. Uniform attractor of the non-autonomous discrete Selkov model. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 229-248. doi: 10.3934/dcds.2014.34.229

[4]

Olivier Goubet, Wided Kechiche. Uniform attractor for non-autonomous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2011, 10 (2) : 639-651. doi: 10.3934/cpaa.2011.10.639

[5]

Sergey Zelik. Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Communications on Pure & Applied Analysis, 2004, 3 (4) : 921-934. doi: 10.3934/cpaa.2004.3.921

[6]

Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087

[7]

Michael Zgurovsky, Mark Gluzman, Nataliia Gorban, Pavlo Kasyanov, Liliia Paliichuk, Olha Khomenko. Uniform global attractors for non-autonomous dissipative dynamical systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 2053-2065. doi: 10.3934/dcdsb.2017120

[8]

Ahmed Y. Abdallah, Rania T. Wannan. Second order non-autonomous lattice systems and their uniform attractors. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1827-1846. doi: 10.3934/cpaa.2019085

[9]

Tomás Caraballo, David Cheban. On the structure of the global attractor for non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2012, 11 (2) : 809-828. doi: 10.3934/cpaa.2012.11.809

[10]

Peter E. Kloeden, José Real, Chunyou Sun. Robust exponential attractors for non-autonomous equations with memory. Communications on Pure & Applied Analysis, 2011, 10 (3) : 885-915. doi: 10.3934/cpaa.2011.10.885

[11]

Bixiang Wang. Multivalued non-autonomous random dynamical systems for wave equations without uniqueness. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 2011-2051. doi: 10.3934/dcdsb.2017119

[12]

Wen Tan. The regularity of pullback attractor for a non-autonomous p-Laplacian equation with dynamical boundary condition. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 529-546. doi: 10.3934/dcdsb.2018194

[13]

Cedric Galusinski, Serguei Zelik. Uniform Gevrey regularity for the attractor of a damped wave equation. Conference Publications, 2003, 2003 (Special) : 305-312. doi: 10.3934/proc.2003.2003.305

[14]

Bixiang Wang. Random attractors for non-autonomous stochastic wave equations with multiplicative noise. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 269-300. doi: 10.3934/dcds.2014.34.269

[15]

Zhijian Yang, Yanan Li. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-14. doi: 10.3934/dcdsb.2019036

[16]

Shengfan Zhou, Min Zhao. Fractal dimension of random attractor for stochastic non-autonomous damped wave equation with linear multiplicative white noise. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2887-2914. doi: 10.3934/dcds.2016.36.2887

[17]

Zhaojuan Wang, Shengfan Zhou. Random attractor and random exponential attractor for stochastic non-autonomous damped cubic wave equation with linear multiplicative white noise. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4767-4817. doi: 10.3934/dcds.2018210

[18]

Alexandre N. Carvalho, José A. Langa, James C. Robinson. Non-autonomous dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 703-747. doi: 10.3934/dcdsb.2015.20.703

[19]

Tomás Caraballo, David Cheban. On the structure of the global attractor for infinite-dimensional non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2013, 12 (1) : 281-302. doi: 10.3934/cpaa.2013.12.281

[20]

Gaocheng Yue. Attractors for non-autonomous reaction-diffusion equations with fractional diffusion in locally uniform spaces. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1645-1671. doi: 10.3934/dcdsb.2017079

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (14)

Other articles
by authors

[Back to Top]