
Previous Article
Minimal dynamics for tree maps
 DCDS Home
 This Issue

Next Article
Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions
Longterm dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent
1.  Department of Mechanics and Mathematics, Kharkov National University, Kharkov, 61077 
2.  Department of Mathematics, University of Virginia, Charlottesville, VA 22903 
3.  Department of Mathematics, University of NebraskaLincoln, Lincoln, NE 68588, United States 
[1] 
Dalibor Pražák. On the dimension of the attractor for the wave equation with nonlinear damping. Communications on Pure & Applied Analysis, 2005, 4 (1) : 165174. doi: 10.3934/cpaa.2005.4.165 
[2] 
Kim Dang Phung. Decay of solutions of the wave equation with localized nonlinear damping and trapped rays. Mathematical Control & Related Fields, 2011, 1 (2) : 251265. doi: 10.3934/mcrf.2011.1.251 
[3] 
Tae Gab Ha. On viscoelastic wave equation with nonlinear boundary damping and source term. Communications on Pure & Applied Analysis, 2010, 9 (6) : 15431576. doi: 10.3934/cpaa.2010.9.1543 
[4] 
Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021015 
[5] 
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) : 119138. doi: 10.3934/dcds.2011.31.119 
[6] 
Aníbal RodríguezBernal, Enrique Zuazua. Parabolic singular limit of a wave equation with localized boundary damping. Discrete & Continuous Dynamical Systems, 1995, 1 (3) : 303346. doi: 10.3934/dcds.1995.1.303 
[7] 
Huafei Di, Yadong Shang, Jiali Yu. Existence and uniform decay estimates for the fourth order wave equation with nonlinear boundary damping and interior source. Electronic Research Archive, 2020, 28 (1) : 221261. doi: 10.3934/era.2020015 
[8] 
Belkacem SaidHouari, Flávio A. Falcão Nascimento. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary dampingsource interaction. Communications on Pure & Applied Analysis, 2013, 12 (1) : 375403. doi: 10.3934/cpaa.2013.12.375 
[9] 
Takeshi Taniguchi. Exponential boundary stabilization for nonlinear wave equations with localized damping and nonlinear boundary condition. Communications on Pure & Applied Analysis, 2017, 16 (5) : 15711585. doi: 10.3934/cpaa.2017075 
[10] 
Jiayun Lin, Kenji Nishihara, Jian Zhai. Critical exponent for the semilinear wave equation with timedependent damping. Discrete & Continuous Dynamical Systems, 2012, 32 (12) : 43074320. doi: 10.3934/dcds.2012.32.4307 
[11] 
Mohamad Darwich. On the $L^2$critical nonlinear Schrödinger Equation with a nonlinear damping. Communications on Pure & Applied Analysis, 2014, 13 (6) : 23772394. doi: 10.3934/cpaa.2014.13.2377 
[12] 
Fathi Hassine. Asymptotic behavior of the transmission EulerBernoulli plate and wave equation with a localized KelvinVoigt damping. Discrete & Continuous Dynamical Systems  B, 2016, 21 (6) : 17571774. doi: 10.3934/dcdsb.2016021 
[13] 
Serge Nicaise, Cristina Pignotti. Stability of the wave equation with localized KelvinVoigt damping and boundary delay feedback. Discrete & Continuous Dynamical Systems  S, 2016, 9 (3) : 791813. doi: 10.3934/dcdss.2016029 
[14] 
Shengfan Zhou, Min Zhao. Fractal dimension of random attractor for stochastic nonautonomous damped wave equation with linear multiplicative white noise. Discrete & Continuous Dynamical Systems, 2016, 36 (5) : 28872914. doi: 10.3934/dcds.2016.36.2887 
[15] 
Giuseppina Autuori, Patrizia Pucci. Kirchhoff systems with nonlinear source and boundary damping terms. Communications on Pure & Applied Analysis, 2010, 9 (5) : 11611188. doi: 10.3934/cpaa.2010.9.1161 
[16] 
Mohammad A. Rammaha, Daniel Toundykov, Zahava Wilstein. Global existence and decay of energy for a nonlinear wave equation with $p$Laplacian damping. Discrete & Continuous Dynamical Systems, 2012, 32 (12) : 43614390. doi: 10.3934/dcds.2012.32.4361 
[17] 
Claudianor O. Alves, M. M. Cavalcanti, Valeria N. Domingos Cavalcanti, Mohammad A. Rammaha, Daniel Toundykov. On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms. Discrete & Continuous Dynamical Systems  S, 2009, 2 (3) : 583608. doi: 10.3934/dcdss.2009.2.583 
[18] 
To Fu Ma, Paulo Nicanor SeminarioHuertas. Attractors for semilinear wave equations with localized damping and external forces. Communications on Pure & Applied Analysis, 2020, 19 (4) : 22192233. doi: 10.3934/cpaa.2020097 
[19] 
Lorena Bociu, Petronela Radu. Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping. Conference Publications, 2009, 2009 (Special) : 6071. doi: 10.3934/proc.2009.2009.60 
[20] 
Gongwei Liu. The existence, general decay and blowup for a plate equation with nonlinear damping and a logarithmic source term. Electronic Research Archive, 2020, 28 (1) : 263289. doi: 10.3934/era.2020016 
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]