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Asymptotic stability of stationary waves for twodimensional viscous conservation laws in half plane
1.  Graduate School of Mathematics, Kyushu University, Fukuoka 8128581, Japan 
2.  Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 1528552, Japan 
3.  Department of Mathematics Sciences, School of Science and Engineering, Waseda University, Tokyo 1698555, Japan 
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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 
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Türker Özsarı, Nermin Yolcu. The initialboundary value problem for the biharmonic Schrödinger equation on the halfline. Communications on Pure and Applied Analysis, 2019, 18 (6) : 32853316. doi: 10.3934/cpaa.2019148 
[4] 
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 
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Yacheng Liu, Runzhang Xu. Potential well method for initial boundary value problem of the generalized double dispersion equations. Communications on Pure and Applied Analysis, 2008, 7 (1) : 6381. doi: 10.3934/cpaa.2008.7.63 
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Linglong Du, Caixuan Ren. Pointwise wave behavior of the initialboundary value problem for the nonlinear damped wave equation in $\mathbb{R}_{+}^{n} $. Discrete and Continuous Dynamical Systems  B, 2019, 24 (7) : 32653280. doi: 10.3934/dcdsb.2018319 
[7] 
Yoshihiro Ueda, Tohru Nakamura, Shuichi Kawashima. Stability of planar stationary waves for damped wave equations with nonlinear convection in multidimensional half space. Kinetic and Related Models, 2008, 1 (1) : 4964. doi: 10.3934/krm.2008.1.49 
[8] 
Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems and Imaging, 2008, 2 (1) : 121131. doi: 10.3934/ipi.2008.2.121 
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Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the halfspace. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957982. doi: 10.3934/cpaa.2007.6.957 
[10] 
Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initialboundary value problem. Conference Publications, 2007, 2007 (Special) : 212220. doi: 10.3934/proc.2007.2007.212 
[11] 
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 
[12] 
Jun Zhou. Initial boundary value problem for a inhomogeneous pseudoparabolic equation. Electronic Research Archive, 2020, 28 (1) : 6790. doi: 10.3934/era.2020005 
[13] 
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 
[14] 
Xianpeng Hu, Dehua Wang. The initialboundary value problem for the compressible viscoelastic flows. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 917934. doi: 10.3934/dcds.2015.35.917 
[15] 
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[16] 
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[17] 
J. Colliander, A. D. Ionescu, C. E. Kenig, Gigliola Staffilani. Weighted lowregularity solutions of the KPI initialvalue problem. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 219258. doi: 10.3934/dcds.2008.20.219 
[18] 
SunHo Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible NavierStokes equation. Networks and Heterogeneous Media, 2013, 8 (2) : 465479. doi: 10.3934/nhm.2013.8.465 
[19] 
Maya Bassam, Denis Mercier, Ali Wehbe. Optimal energy decay rate of Rayleigh beam equation with only one boundary control force. Evolution Equations and Control Theory, 2015, 4 (1) : 2138. doi: 10.3934/eect.2015.4.21 
[20] 
Imen Manoubi. Theoretical and numerical analysis of the decay rate of solutions to a water wave model with a nonlocal viscous dispersive term with RiemannLiouville half derivative. Discrete and Continuous Dynamical Systems  B, 2014, 19 (9) : 28372863. doi: 10.3934/dcdsb.2014.19.2837 
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