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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 & Continuous Dynamical Systems  A, 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 & 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 & 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 & 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 & Continuous Dynamical Systems  A, 2011, 31 (1) : 119138. doi: 10.3934/dcds.2011.31.119 
[8] 
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 
[9] 
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 
[10] 
Peter V. Gordon, Cyrill B. Muratov. Selfsimilarity and longtime behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source. Networks & Heterogeneous Media, 2012, 7 (4) : 767780. doi: 10.3934/nhm.2012.7.767 
[11] 
A. Kh. Khanmamedov. Longtime behaviour of wave equations with nonlinear interior damping. Discrete & Continuous Dynamical Systems  A, 2008, 21 (4) : 11851198. doi: 10.3934/dcds.2008.21.1185 
[12] 
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 
[13] 
JongShenq Guo, Bei Hu. Blowup rate estimates for the heat equation with a nonlinear gradient source term. Discrete & Continuous Dynamical Systems  A, 2008, 20 (4) : 927937. doi: 10.3934/dcds.2008.20.927 
[14] 
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 
[15] 
Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finitetime blowup for a Schrödinger equation with nonlinear source term. Discrete & Continuous Dynamical Systems  A, 2019, 39 (2) : 11711183. doi: 10.3934/dcds.2019050 
[16] 
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 
[17] 
Jiayun Lin, Kenji Nishihara, Jian Zhai. Critical exponent for the semilinear wave equation with timedependent damping. Discrete & Continuous Dynamical Systems  A, 2012, 32 (12) : 43074320. doi: 10.3934/dcds.2012.32.4307 
[18] 
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 
[19] 
Yacheng Liu, Runzhang Xu. Wave equations and reactiondiffusion equations with several nonlinear source terms of different sign. Discrete & Continuous Dynamical Systems  B, 2007, 7 (1) : 171189. doi: 10.3934/dcdsb.2007.7.171 
[20] 
Nicolas Fourrier, Irena Lasiecka. Regularity and stability of a wave equation with a strong damping and dynamic boundary conditions. Evolution Equations & Control Theory, 2013, 2 (4) : 631667. doi: 10.3934/eect.2013.2.631 
2019 Impact Factor: 1.338
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