American Institute of Mathematical Sciences

Advanced
  • Previous Article
    A nonlinear controlled system of differential equations describing the process of production and sales of a consumer good
  • PROC Home
  • This Issue
  • Next Article
    Oscillatory properties of third order neutral delay differential equations
2003, 2003(Special): 351-358. doi: 10.3934/proc.2003.2003.351

On the damped semilinear wave equation with critical exponent

Maurizio Grasselli 1, and  Vittorino Pata 2,

1. 

Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano, Italy
2. 

Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received  June 2002 Revised  March 2003 Published  April 2003

We provide an optimal regularity result for the universal attractor of the weakly damped semilinear wave equation, when the nonlinearity satisfies the critical growth condition. This allows us to prove an upper semicontinuity result as well as the existence of an exponential attractor.
Keywords: exponential attractors., upper semicontinuity, Damped wave equation, universal attractors.
Mathematics Subject Classification: Primary: 35B41, 35L05; Secondary: 35L25, 35Q4.
Citation: Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351
[1]

Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2787-2812. doi: 10.3934/dcds.2017120
[2]

Pierre Fabrie, Cedric Galusinski, A. Miranville, Sergey Zelik. Uniform exponential attractors for a singularly perturbed damped wave equation. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 211-238. doi: 10.3934/dcds.2004.10.211
[3]

Yonghai Wang, Chengkui Zhong. Upper semicontinuity of pullback attractors for nonautonomous Kirchhoff wave models. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3189-3209. doi: 10.3934/dcds.2013.33.3189
[4]

Zhijian Yang, Yanan Li. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4899-4912. doi: 10.3934/dcdsb.2019036
[5]

Yonghai Wang. On the upper semicontinuity of pullback attractors with applications to plate equations. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1653-1673. doi: 10.3934/cpaa.2010.9.1653
[6]

Linfang Liu, Xianlong Fu. Existence and upper semicontinuity of (L2, Lq) pullback attractors for a stochastic p-laplacian equation. Communications on Pure and Applied Analysis, 2017, 6 (2) : 443-474. doi: 10.3934/cpaa.2017023
[7]

Ling Xu, Jianhua Huang, Qiaozhen Ma. Upper semicontinuity of random attractors for the stochastic non-autonomous suspension bridge equation with memory. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 5959-5979. doi: 10.3934/dcdsb.2019115
[8]

Matheus C. Bortolan, José Manuel Uzal. Upper and weak-lower semicontinuity of pullback attractors to impulsive evolution processes. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3667-3692. doi: 10.3934/dcdsb.2020252
[9]

Pengyan Ding, Zhijian Yang. Attractors of the strongly damped Kirchhoff wave equation on $\mathbb{R}^{N}$. Communications on Pure and Applied Analysis, 2019, 18 (2) : 825-843. doi: 10.3934/cpaa.2019040
[10]

John M. Ball. Global attractors for damped semilinear wave equations. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 31-52. doi: 10.3934/dcds.2004.10.31
[11]

Kei Matsuura, Mitsuharu Otani. Exponential attractors for a quasilinear parabolic equation. Conference Publications, 2007, 2007 (Special) : 713-720. doi: 10.3934/proc.2007.2007.713
[12]

Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of attractors for non-autonomous stochastic lattice systems with random coupled coefficients. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2221-2245. doi: 10.3934/cpaa.2016035
[13]

Yejuan Wang. On the upper semicontinuity of pullback attractors for multi-valued noncompact random dynamical systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3669-3708. doi: 10.3934/dcdsb.2016116
[14]

Wenlong Sun. The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay. Electronic Research Archive, 2020, 28 (3) : 1343-1356. doi: 10.3934/era.2020071
[15]

Na Lei, Shengfan Zhou. Upper semicontinuity of pullback attractors for non-autonomous lattice systems under singular perturbations. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 73-108. doi: 10.3934/dcds.2021108
[16]

Xinyu Mei, Chunyou Sun. Attractors for A sup-cubic weakly damped wave equation in $ \mathbb{R}^{3} $. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4117-4143. doi: 10.3934/dcdsb.2019053
[17]

Qingquan Chang, Dandan Li, Chunyou Sun. Random attractors for stochastic time-dependent damped wave equation with critical exponents. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2793-2824. doi: 10.3934/dcdsb.2020033
[18]

Kaixuan Zhu, Yongqin Xie, Xinyu Mei. Pullback attractors for a weakly damped wave equation with delays and sup-cubic nonlinearity. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4433-4458. doi: 10.3934/dcdsb.2020294
[19]

Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 559-566. doi: 10.3934/dcdss.2012.5.559
[20]

Filippo Dell'Oro. Global attractors for strongly damped wave equations with subcritical-critical nonlinearities. Communications on Pure and Applied Analysis, 2013, 12 (2) : 1015-1027. doi: 10.3934/cpaa.2013.12.1015

 Impact Factor: 

Tools

Metrics

  • PDF downloads (101)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy