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On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms
Higher order energy decay rates for damped wave equations with variable coefficients
1.  Department of Mathematics, University of NebraskaLincoln, Avery Hall 239, Lincoln, NE 68588, United States 
2.  Department of Mathematics, University of Tennessee, Knoxville, TN 370961300 
3.  Department of Mathematics, University of TennesseeKnoxville, TN 37996, United States 
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Jun Zhou. Global existence and energy decay estimate of solutions for a class of nonlinear higherorder wave equation with general nonlinear dissipation and source term. Discrete & Continuous Dynamical Systems  S, 2017, 10 (5) : 11751185. doi: 10.3934/dcdss.2017064 
[2] 
Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations & Control Theory, 2016, 5 (1) : 3759. doi: 10.3934/eect.2016.5.37 
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Ryo Ikehata, Shingo Kitazaki. Optimal energy decay rates for some wave equations with double damping terms. Evolution Equations & Control Theory, 2019, 8 (4) : 825846. doi: 10.3934/eect.2019040 
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Shikuan Mao, Yongqin Liu. Decay property for solutions to plate type equations with variable coefficients. Kinetic & Related Models, 2017, 10 (3) : 785797. doi: 10.3934/krm.2017031 
[5] 
Moez Daoulatli, Irena Lasiecka, Daniel Toundykov. Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions. Discrete & Continuous Dynamical Systems  S, 2009, 2 (1) : 6794. doi: 10.3934/dcdss.2009.2.67 
[6] 
Hiroshi Takeda. Global existence of solutions for higher order nonlinear damped wave equations. Conference Publications, 2011, 2011 (Special) : 13581367. doi: 10.3934/proc.2011.2011.1358 
[7] 
Moez Daoulatli. Rates of decay for the wave systems with time dependent damping. Discrete & Continuous Dynamical Systems  A, 2011, 31 (2) : 407443. doi: 10.3934/dcds.2011.31.407 
[8] 
Montgomery Taylor. The diffusion phenomenon for damped wave equations with spacetime dependent coefficients. Discrete & Continuous Dynamical Systems  A, 2018, 38 (11) : 59215941. doi: 10.3934/dcds.2018257 
[9] 
Larissa V. Fardigola. Transformation operators in controllability problems for the wave equations with variable coefficients on a halfaxis controlled by the Dirichlet boundary condition. Mathematical Control & Related Fields, 2015, 5 (1) : 3153. doi: 10.3934/mcrf.2015.5.31 
[10] 
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 
[11] 
JunRen Luo, TiJun Xiao. Decay rates for second order evolution equations in Hilbert spaces with nonlinear timedependent damping. Evolution Equations & Control Theory, 2019, 0 (0) : 00. doi: 10.3934/eect.2020009 
[12] 
Zdeněk Skalák. On the asymptotic decay of higherorder norms of the solutions to the NavierStokes equations in R^{3}. Discrete & Continuous Dynamical Systems  S, 2010, 3 (2) : 361370. doi: 10.3934/dcdss.2010.3.361 
[13] 
Rachid Assel, Mohamed Ghazel. Energy decay for the damped wave equation on an unbounded network. Evolution Equations & Control Theory, 2018, 7 (3) : 335351. doi: 10.3934/eect.2018017 
[14] 
Ruy Coimbra Charão, Jáuber Cavalcante Oliveira, Gustavo Alberto Perla Menzala. Energy decay rates of magnetoelastic waves in a bounded conductive medium. Discrete & Continuous Dynamical Systems  A, 2009, 25 (3) : 797821. doi: 10.3934/dcds.2009.25.797 
[15] 
Jibin Li, Weigou Rui, Yao Long, Bin He. Travelling wave solutions for higherorder wave equations of KDV type (III). Mathematical Biosciences & Engineering, 2006, 3 (1) : 125135. doi: 10.3934/mbe.2006.3.125 
[16] 
Louis Tebou. Energy decay estimates for some weakly coupled EulerBernoulli and wave equations with indirect damping mechanisms. Mathematical Control & Related Fields, 2012, 2 (1) : 4560. doi: 10.3934/mcrf.2012.2.45 
[17] 
Mohammed Aassila. On energy decay rate for linear damped systems. Discrete & Continuous Dynamical Systems  A, 2002, 8 (4) : 851864. doi: 10.3934/dcds.2002.8.851 
[18] 
Henri Schurz. Dissipation of mean energy of discretized linear oscillators under random perturbations. Conference Publications, 2005, 2005 (Special) : 778783. doi: 10.3934/proc.2005.2005.778 
[19] 
Santiago Montaner, Arnaud Münch. Approximation of controls for linear wave equations: A first order mixed formulation. Mathematical Control & Related Fields, 2019, 0 (0) : 00. doi: 10.3934/mcrf.2019030 
[20] 
Wenming Hu, Huicheng Yin. Wellposedness of low regularity solutions to the second order strictly hyperbolic equations with nonLipschitzian coefficients. Communications on Pure & Applied Analysis, 2019, 18 (4) : 18911919. doi: 10.3934/cpaa.2019088 
2018 Impact Factor: 0.545
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