# American Institute of Mathematical Sciences

November  2008, 21(4): 1185-1198. doi: 10.3934/dcds.2008.21.1185

## Long-time behaviour of wave equations with nonlinear interior damping

 1 Department of Mathematics, Faculty of Science, Hacettepe University, Beytepe 06532, Ankara, Turkey

Received  October 2007 Revised  March 2008 Published  May 2008

We prove the existence of attractors for higher dimensional wave equations with nonlinear interior damping which grows faster than polynomials at infinity.
Citation: A. Kh. Khanmamedov. Long-time behaviour of wave equations with nonlinear interior damping. Discrete & Continuous Dynamical Systems, 2008, 21 (4) : 1185-1198. doi: 10.3934/dcds.2008.21.1185
 [1] Jean Ginibre, Giorgio Velo. Modified wave operators without loss of regularity for some long range Hartree equations. II. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1357-1376. doi: 10.3934/cpaa.2015.14.1357 [2] John M. Ball. Global attractors for damped semilinear wave equations. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 31-52. doi: 10.3934/dcds.2004.10.31 [3] Bixiang Wang, Xiaoling Gao. Random attractors for wave equations on unbounded domains. Conference Publications, 2009, 2009 (Special) : 800-809. doi: 10.3934/proc.2009.2009.800 [4] Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks & Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007 [5] To Fu Ma, Paulo Nicanor Seminario-Huertas. Attractors for semilinear wave equations with localized damping and external forces. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2219-2233. doi: 10.3934/cpaa.2020097 [6] Bixiang Wang. Random attractors for non-autonomous stochastic wave equations with multiplicative noise. Discrete & Continuous Dynamical Systems, 2014, 34 (1) : 269-300. doi: 10.3934/dcds.2014.34.269 [7] Filippo Dell'Oro. Global attractors for strongly damped wave equations with subcritical-critical nonlinearities. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1015-1027. doi: 10.3934/cpaa.2013.12.1015 [8] Zhijian Yang, Yanan Li. Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4899-4912. doi: 10.3934/dcdsb.2019036 [9] Fengjuan Meng, Meihua Yang, Chengkui Zhong. Attractors for wave equations with nonlinear damping on time-dependent space. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 205-225. doi: 10.3934/dcdsb.2016.21.205 [10] Renhai Wang, Yangrong Li. Backward compactness and periodicity of random attractors for stochastic wave equations with varying coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4145-4167. doi: 10.3934/dcdsb.2019054 [11] Veronica Belleri, Vittorino Pata. Attractors for semilinear strongly damped wave equations on $\mathbb R^3$. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 719-735. doi: 10.3934/dcds.2001.7.719 [12] Sergey Dashkovskiy, Oleksiy Kapustyan. Robustness of global attractors: Abstract framework and application to dissipative wave equations. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021054 [13] Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems & Imaging, 2016, 10 (4) : 869-898. doi: 10.3934/ipi.2016025 [14] Mohamed Assellaou, Olivier Bokanowski, Hasnaa Zidani. Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 3933-3964. doi: 10.3934/dcds.2015.35.3933 [15] Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001 [16] A. Kh. Khanmamedov. Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 119-138. doi: 10.3934/dcds.2011.31.119 [17] Xiaohu Wang, Dingshi Li, Jun Shen. Wong-Zakai approximations and attractors for stochastic wave equations driven by additive noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2829-2855. doi: 10.3934/dcdsb.2020207 [18] Björn Birnir, Kenneth Nelson. The existence of smooth attractors of damped and driven nonlinear wave equations with critical exponent , s = 5. Conference Publications, 1998, 1998 (Special) : 100-117. doi: 10.3934/proc.1998.1998.100 [19] Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems & Imaging, 2013, 7 (2) : 307-340. doi: 10.3934/ipi.2013.7.307 [20] Michael Dellnitz, Mirko Hessel-Von Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93-112. doi: 10.3934/jcd.2016005

2020 Impact Factor: 1.392