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On small amplitude solutions to the generalized Boussinesq equations
1. | Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan |
[1] |
J. Colliander, Justin Holmer, Monica Visan, Xiaoyi Zhang. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure and Applied Analysis, 2008, 7 (3) : 467-489. doi: 10.3934/cpaa.2008.7.467 |
[2] |
Walter A. Strauss, Kimitoshi Tsutaya. Existence and blow up of small amplitude nonlinear waves with a negative potential. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 175-188. doi: 10.3934/dcds.1997.3.175 |
[3] |
Guy Métivier, K. Zumbrun. Existence and sharp localization in velocity of small-amplitude Boltzmann shocks. Kinetic and Related Models, 2009, 2 (4) : 667-705. doi: 10.3934/krm.2009.2.667 |
[4] |
Kosuke Ono. Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 651-662. doi: 10.3934/dcds.2003.9.651 |
[5] |
Reinhard Racke, Jürgen Saal. Hyperbolic Navier-Stokes equations II: Global existence of small solutions. Evolution Equations and Control Theory, 2012, 1 (1) : 217-234. doi: 10.3934/eect.2012.1.217 |
[6] |
Ling Liu, Jiashan Zheng. Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3357-3377. doi: 10.3934/dcdsb.2018324 |
[7] |
Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa. On small data scattering of Hartree equations with short-range interaction. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1809-1823. doi: 10.3934/cpaa.2016016 |
[8] |
Changhun Yang. Scattering results for Dirac Hartree-type equations with small initial data. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1711-1734. doi: 10.3934/cpaa.2019081 |
[9] |
Shubin Wang, Guowang Chen. Cauchy problem for the nonlinear Schrödinger-IMBq equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 203-214. doi: 10.3934/dcdsb.2006.6.203 |
[10] |
Laiqing Meng, Jia Yuan, Xiaoxin Zheng. Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3413-3441. doi: 10.3934/dcds.2019141 |
[11] |
Victor Wasiolek. Uniform global existence and convergence of Euler-Maxwell systems with small parameters. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2007-2021. doi: 10.3934/cpaa.2016025 |
[12] |
Roger Grimshaw, Dmitry Pelinovsky. Global existence of small-norm solutions in the reduced Ostrovsky equation. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 557-566. doi: 10.3934/dcds.2014.34.557 |
[13] |
Anudeep Kumar Arora. Scattering of radial data in the focusing NLS and generalized Hartree equations. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6643-6668. doi: 10.3934/dcds.2019289 |
[14] |
Dimitra Antonopoulou, Georgia Karali. Existence of solution for a generalized stochastic Cahn-Hilliard equation on convex domains. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 31-55. doi: 10.3934/dcdsb.2011.16.31 |
[15] |
Rodica Toader. Scattering in domains with many small obstacles. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 321-338. doi: 10.3934/dcds.1998.4.321 |
[16] |
Fabio Scalco Dias, Luis Fernando Mello. The center--focus problem and small amplitude limit cycles in rigid systems. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1627-1637. doi: 10.3934/dcds.2012.32.1627 |
[17] |
Ling-Jun Wang. The dynamics of small amplitude solutions of the Swift-Hohenberg equation on a large interval. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1129-1156. doi: 10.3934/cpaa.2012.11.1129 |
[18] |
Andrew Comech, David Stuart. Small amplitude solitary waves in the Dirac-Maxwell system. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1349-1370. doi: 10.3934/cpaa.2018066 |
[19] |
Deconinck Bernard, Olga Trichtchenko. High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1323-1358. doi: 10.3934/dcds.2017055 |
[20] |
Ramon Plaza, K. Zumbrun. An Evans function approach to spectral stability of small-amplitude shock profiles. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 885-924. doi: 10.3934/dcds.2004.10.885 |
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