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Potential well method for initial boundary value problem of the generalized double dispersion equations
1.  College of Science, Harbin Engineering University, Harbin, 150001, China, China 
[1] 
Yang Liu, Wenke Li. A family of potential wells for a wave equation. Electronic Research Archive, 2020, 28 (2) : 807820. doi: 10.3934/era.2020041 
[2] 
Shaoyong Lai, Yong Hong Wu, Xu Yang. The global solution of an initial boundary value problem for the damped Boussinesq equation. Communications on Pure and Applied Analysis, 2004, 3 (2) : 319328. doi: 10.3934/cpaa.2004.3.319 
[3] 
Fei Guo, BaoFeng Feng, Hongjun Gao, Yue Liu. On the initialvalue problem to the DegasperisProcesi equation with linear dispersion. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 12691290. doi: 10.3934/dcds.2010.26.1269 
[4] 
JongShenq Guo, Masahiko Shimojo. Blowing up at zero points of potential for an initial boundary value problem. Communications on Pure and Applied Analysis, 2011, 10 (1) : 161177. doi: 10.3934/cpaa.2011.10.161 
[5] 
Eric R. Kaufmann. Existence and nonexistence of positive solutions for a nonlinear fractional boundary value problem. Conference Publications, 2009, 2009 (Special) : 416423. doi: 10.3934/proc.2009.2009.416 
[6] 
Vladimir V. Varlamov. On the initial boundary value problem for the damped Boussinesq equation. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 431444. doi: 10.3934/dcds.1998.4.431 
[7] 
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 
[8] 
Xu Liu, Jun Zhou. Initialboundary value problem for a fourthorder plate equation with HardyHénon potential and polynomial nonlinearity. Electronic Research Archive, 2020, 28 (2) : 599625. doi: 10.3934/era.2020032 
[9] 
Jing Li, Boling Guo, Lan Zeng, Yitong Pei. Global weak solution and smooth solution of the periodic initial value problem for the generalized LandauLifshitzBloch equation in high dimensions. Discrete and Continuous Dynamical Systems  B, 2020, 25 (4) : 13451360. doi: 10.3934/dcdsb.2019230 
[10] 
Masakazu Kato, YuZhu Wang, Shuichi Kawashima. Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension. Kinetic and Related Models, 2013, 6 (4) : 969987. doi: 10.3934/krm.2013.6.969 
[11] 
Ivonne Rivas, Muhammad Usman, BingYu Zhang. Global wellposedness and asymptotic behavior of a class of initialboundaryvalue problem of the KortewegDe Vries equation on a finite domain. Mathematical Control and Related Fields, 2011, 1 (1) : 6181. doi: 10.3934/mcrf.2011.1.61 
[12] 
Xie Li, Zhaoyin Xiang. Existence and nonexistence of local/global solutions for a nonhomogeneous heat equation. Communications on Pure and Applied Analysis, 2014, 13 (4) : 14651480. doi: 10.3934/cpaa.2014.13.1465 
[13] 
Yuxuan Chen, Jiangbo Han. Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level. Discrete and Continuous Dynamical Systems  S, 2021, 14 (12) : 41794200. doi: 10.3934/dcdss.2021109 
[14] 
Changming Song, Hong Li, Jina Li. Initial boundary value problem for the singularly perturbed Boussinesqtype equation. Conference Publications, 2013, 2013 (special) : 709717. doi: 10.3934/proc.2013.2013.709 
[15] 
Jun Zhou. Initial boundary value problem for a inhomogeneous pseudoparabolic equation. Electronic Research Archive, 2020, 28 (1) : 6790. doi: 10.3934/era.2020005 
[16] 
Hui Yang, Yuzhu Han. Initial boundary value problem for a strongly damped wave equation with a general nonlinearity. Evolution Equations and Control Theory, 2022, 11 (3) : 635648. doi: 10.3934/eect.2021019 
[17] 
Yuxia Guo, Zhongwei Tang. Multibump solutions for Schrödinger equation involving critical growth and potential wells. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 33933415. doi: 10.3934/dcds.2015.35.3393 
[18] 
Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initialboundary value problem of a 2D KazhikhovSmagulov type model. Discrete and Continuous Dynamical Systems  S, 2014, 7 (5) : 917923. doi: 10.3934/dcdss.2014.7.917 
[19] 
Peng Jiang. Unique global solution of an initialboundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 30153037. doi: 10.3934/dcds.2015.35.3015 
[20] 
Tatsien Li, Libin Wang. Global classical solutions to a kind of mixed initialboundary value problem for quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 5978. doi: 10.3934/dcds.2005.12.59 
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