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Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping
1.  University of NebraskaLincoln, Lincoln, NC 685880130, United States 
2.  Department of Mathematics, University of NebraskaLincoln, Avery Hall 239, Lincoln, NE 68588 
[1] 
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 and Continuous Dynamical Systems  S, 2009, 2 (3) : 583608. doi: 10.3934/dcdss.2009.2.583 
[2] 
Ryo Ikehata, Shingo Kitazaki. Optimal energy decay rates for some wave equations with double damping terms. Evolution Equations and Control Theory, 2019, 8 (4) : 825846. doi: 10.3934/eect.2019040 
[3] 
Lorena Bociu, Irena Lasiecka. Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 835860. doi: 10.3934/dcds.2008.22.835 
[4] 
Giuseppina Autuori, Patrizia Pucci. Kirchhoff systems with nonlinear source and boundary damping terms. Communications on Pure and Applied Analysis, 2010, 9 (5) : 11611188. doi: 10.3934/cpaa.2010.9.1161 
[5] 
Vo Anh Khoa, Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence, blowup and exponential decay of solutions for a porouselastic system with damping and source terms. Evolution Equations and Control Theory, 2019, 8 (2) : 359395. doi: 10.3934/eect.2019019 
[6] 
Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations and Control Theory, 2016, 5 (1) : 3759. doi: 10.3934/eect.2016.5.37 
[7] 
Yacheng Liu, Runzhang Xu. Wave equations and reactiondiffusion equations with several nonlinear source terms of different sign. Discrete and Continuous Dynamical Systems  B, 2007, 7 (1) : 171189. doi: 10.3934/dcdsb.2007.7.171 
[8] 
A. Kh. Khanmamedov. Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 119138. doi: 10.3934/dcds.2011.31.119 
[9] 
Makoto Nakamura. Remarks on global solutions of dissipative wave equations with exponential nonlinear terms. Communications on Pure and Applied Analysis, 2015, 14 (4) : 15331545. doi: 10.3934/cpaa.2015.14.1533 
[10] 
Genni Fragnelli, Dimitri Mugnai. Stability of solutions for nonlinear wave equations with a positivenegative damping. Discrete and Continuous Dynamical Systems  S, 2011, 4 (3) : 615622. doi: 10.3934/dcdss.2011.4.615 
[11] 
Marcello D'Abbicco. Small data solutions for semilinear wave equations with effective damping. Conference Publications, 2013, 2013 (special) : 183191. doi: 10.3934/proc.2013.2013.183 
[12] 
Louis Tebou. Energy decay estimates for some weakly coupled EulerBernoulli and wave equations with indirect damping mechanisms. Mathematical Control and Related Fields, 2012, 2 (1) : 4560. doi: 10.3934/mcrf.2012.2.45 
[13] 
Chao Yang, Yanbing Yang. Longtime behavior for fourthorder wave equations with strain term and nonlinear weak damping term. Discrete and Continuous Dynamical Systems  S, 2021, 14 (12) : 46434658. doi: 10.3934/dcdss.2021110 
[14] 
Abdelaziz Soufyane, Belkacem SaidHouari. The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system. Evolution Equations and Control Theory, 2014, 3 (4) : 713738. doi: 10.3934/eect.2014.3.713 
[15] 
Tae Gab Ha. On viscoelastic wave equation with nonlinear boundary damping and source term. Communications on Pure and Applied Analysis, 2010, 9 (6) : 15431576. doi: 10.3934/cpaa.2010.9.1543 
[16] 
Carlos E. Kenig, Frank Merle. Radial solutions to energy supercritical wave equations in odd dimensions. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 13651381. doi: 10.3934/dcds.2011.31.1365 
[17] 
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 and Continuous Dynamical Systems  S, 2017, 10 (5) : 11751185. doi: 10.3934/dcdss.2017064 
[18] 
Daniel Pardo, José Valero, Ángel Giménez. Global attractors for weak solutions of the threedimensional NavierStokes equations with damping. Discrete and Continuous Dynamical Systems  B, 2019, 24 (8) : 35693590. doi: 10.3934/dcdsb.2018279 
[19] 
Fang Li, Bo You, Yao Xu. Dynamics of weak solutions for the three dimensional NavierStokes equations with nonlinear damping. Discrete and Continuous Dynamical Systems  B, 2018, 23 (10) : 42674284. doi: 10.3934/dcdsb.2018137 
[20] 
Andrew R. Becklin, Mohammad A. Rammaha. Hadamard wellposedness for a structure acoustic model with a supercritical source and damping terms. Evolution Equations and Control Theory, 2021, 10 (4) : 797836. doi: 10.3934/eect.2020093 
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