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Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping
1.  Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States, United States 
[1] 
Igor Chueshov, Irena Lasiecka, Daniel Toundykov. Longterm dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 459509. doi: 10.3934/dcds.2008.20.459 
[2] 
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 
[3] 
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 
[4] 
Belkacem SaidHouari, Flávio A. Falcão Nascimento. Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary dampingsource interaction. Communications on Pure and Applied Analysis, 2013, 12 (1) : 375403. doi: 10.3934/cpaa.2013.12.375 
[5] 
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 
[6] 
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 
[7] 
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 
[8] 
Enzo Vitillaro. Blow–up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources. Discrete and Continuous Dynamical Systems  S, 2021, 14 (12) : 45754608. doi: 10.3934/dcdss.2021130 
[9] 
Nadjat Doudi, Salah Boulaaras, Nadia Mezouar, Rashid Jan. Global existence, general decay and blowup for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation. Discrete and Continuous Dynamical Systems  S, 2022 doi: 10.3934/dcdss.2022106 
[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 and Continuous Dynamical Systems  S, 2009, 2 (3) : 583608. doi: 10.3934/dcdss.2009.2.583 
[11] 
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 
[12] 
Mohammad AlGharabli, Mohamed Balegh, Baowei Feng, Zayd Hajjej, Salim A. Messaoudi. Existence and general decay of BalakrishnanTaylor viscoelastic equation with nonlinear frictional damping and logarithmic source term. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021038 
[13] 
Xiaoli Feng, Meixia Zhao, Peijun Li, Xu Wang. An inverse source problem for the stochastic wave equation. Inverse Problems and Imaging, 2022, 16 (2) : 397415. doi: 10.3934/ipi.2021055 
[14] 
Peter V. Gordon, Cyrill B. Muratov. Selfsimilarity and longtime behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source. Networks and Heterogeneous Media, 2012, 7 (4) : 767780. doi: 10.3934/nhm.2012.7.767 
[15] 
A. Kh. Khanmamedov. Longtime behaviour of wave equations with nonlinear interior damping. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 11851198. doi: 10.3934/dcds.2008.21.1185 
[16] 
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 
[17] 
JongShenq Guo, Bei Hu. Blowup rate estimates for the heat equation with a nonlinear gradient source term. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 927937. doi: 10.3934/dcds.2008.20.927 
[18] 
Xuan Liu, Ting Zhang. $ H^2 $ blowup result for a Schrödinger equation with nonlinear source term. Electronic Research Archive, 2020, 28 (2) : 777794. doi: 10.3934/era.2020039 
[19] 
Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finitetime blowup for a Schrödinger equation with nonlinear source term. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 11711183. doi: 10.3934/dcds.2019050 
[20] 
Dalibor Pražák. On the dimension of the attractor for the wave equation with nonlinear damping. Communications on Pure and Applied Analysis, 2005, 4 (1) : 165174. doi: 10.3934/cpaa.2005.4.165 
2020 Impact Factor: 1.392
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