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Attractors for noncompact nonautonomous systems via energy equations
1. | Department of Mathematics, University of Texas at Austin, Austin, TX 78712, United States |
2. | Department of Applied Mathematics, Federal University of Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ 21945–970 |
3. | Department of Mathematics, Iowa State University, Ames, IA 50011, United States |
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Eduardo Cerpa. Control of a Korteweg-de Vries equation: A tutorial. Mathematical Control and Related Fields, 2014, 4 (1) : 45-99. doi: 10.3934/mcrf.2014.4.45 |
[2] |
M. Agrotis, S. Lafortune, P.G. Kevrekidis. On a discrete version of the Korteweg-De Vries equation. Conference Publications, 2005, 2005 (Special) : 22-29. doi: 10.3934/proc.2005.2005.22 |
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C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 403-429. doi: 10.3934/dcds.2001.7.403 |
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Julie Valein. On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021039 |
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Olivier Goubet. Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 625-644. doi: 10.3934/dcds.2000.6.625 |
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Cung The Anh, Dang Thi Phuong Thanh, Nguyen Duong Toan. Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces. Evolution Equations and Control Theory, 2021, 10 (1) : 1-23. doi: 10.3934/eect.2020039 |
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Songsong Lu, Hongqing Wu, Chengkui Zhong. Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces. Discrete and Continuous Dynamical Systems, 2005, 13 (3) : 701-719. doi: 10.3934/dcds.2005.13.701 |
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Guolian Wang, Boling Guo. Stochastic Korteweg-de Vries equation driven by fractional Brownian motion. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5255-5272. doi: 10.3934/dcds.2015.35.5255 |
[9] |
Zhaosheng Feng, Yu Huang. Approximate solution of the Burgers-Korteweg-de Vries equation. Communications on Pure and Applied Analysis, 2007, 6 (2) : 429-440. doi: 10.3934/cpaa.2007.6.429 |
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Muhammad Usman, Bing-Yu Zhang. Forced oscillations of the Korteweg-de Vries equation on a bounded domain and their stability. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1509-1523. doi: 10.3934/dcds.2010.26.1509 |
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Eduardo Cerpa, Emmanuelle Crépeau. Rapid exponential stabilization for a linear Korteweg-de Vries equation. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 655-668. doi: 10.3934/dcdsb.2009.11.655 |
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Pierre Garnier. Damping to prevent the blow-up of the korteweg-de vries equation. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1455-1470. doi: 10.3934/cpaa.2017069 |
[13] |
Massimiliano Gubinelli. Rough solutions for the periodic Korteweg--de~Vries equation. Communications on Pure and Applied Analysis, 2012, 11 (2) : 709-733. doi: 10.3934/cpaa.2012.11.709 |
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Ahmat Mahamat Taboye, Mohamed Laabissi. Exponential stabilization of a linear Korteweg-de Vries equation with input saturation. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021052 |
[15] |
Terence Tao. Two remarks on the generalised Korteweg de-Vries equation. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 1-14. doi: 10.3934/dcds.2007.18.1 |
[16] |
Ivonne Rivas, Muhammad Usman, Bing-Yu Zhang. Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control and Related Fields, 2011, 1 (1) : 61-81. doi: 10.3934/mcrf.2011.1.61 |
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P.E. Kloeden, Victor S. Kozyakin. Uniform nonautonomous attractors under discretization. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 423-433. doi: 10.3934/dcds.2004.10.423 |
[18] |
Peter Anthony, Sergey Zelik. Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1361-1393. doi: 10.3934/cpaa.2014.13.1361 |
[19] |
Xiangming Zhu, Chengkui Zhong. Uniform attractors for nonautonomous reaction-diffusion equations with the nonlinearity in a larger symbol space. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021212 |
[20] |
Xue-Li Song, Yan-Ren Hou. Attractors for the three-dimensional incompressible Navier-Stokes equations with damping. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 239-252. doi: 10.3934/dcds.2011.31.239 |
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