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The existence of a global attractor for a Kuramoto-Sivashinsky type equation in 2D
1. | Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, United States |
[1] |
Kiah Wah Ong. Dynamic transitions of generalized Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1225-1236. doi: 10.3934/dcdsb.2016.21.1225 |
[2] |
Milena Stanislavova, Atanas Stefanov. Effective estimates of the higher Sobolev norms for the Kuramoto-Sivashinsky equation. Conference Publications, 2009, 2009 (Special) : 729-738. doi: 10.3934/proc.2009.2009.729 |
[3] |
Jared C. Bronski, Razvan C. Fetecau, Thomas N. Gambill. A note on a non-local Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 701-707. doi: 10.3934/dcds.2007.18.701 |
[4] |
Peng Gao. Averaging principle for stochastic Kuramoto-Sivashinsky equation with a fast oscillation. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5649-5684. doi: 10.3934/dcds.2018247 |
[5] |
Eduardo Cerpa. Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation. Communications on Pure and Applied Analysis, 2010, 9 (1) : 91-102. doi: 10.3934/cpaa.2010.9.91 |
[6] |
D. Hilhorst, L. A. Peletier, A. I. Rotariu, G. Sivashinsky. Global attractor and inertial sets for a nonlocal Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 557-580. doi: 10.3934/dcds.2004.10.557 |
[7] |
Piotr Zgliczyński. Steady state bifurcations for the Kuramoto-Sivashinsky equation: A computer assisted proof. Journal of Computational Dynamics, 2015, 2 (1) : 95-142. doi: 10.3934/jcd.2015.2.95 |
[8] |
Yuncherl Choi, Jongmin Han, Chun-Hsiung Hsia. Bifurcation analysis of the damped Kuramoto-Sivashinsky equation with respect to the period. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 1933-1957. doi: 10.3934/dcdsb.2015.20.1933 |
[9] |
L. Dieci, M. S Jolly, Ricardo Rosa, E. S. Van Vleck. Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 555-580. doi: 10.3934/dcdsb.2008.9.555 |
[10] |
Peng Gao. Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation. Evolution Equations and Control Theory, 2020, 9 (1) : 181-191. doi: 10.3934/eect.2020002 |
[11] |
Shuting Chen, Zengji Du, Jiang Liu, Ke Wang. The dynamic properties of a generalized Kawahara equation with Kuramoto-Sivashinsky perturbation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1471-1496. doi: 10.3934/dcdsb.2021098 |
[12] |
Yangrong Li, Shuang Yang, Qiangheng Zhang. Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation. Electronic Research Archive, 2020, 28 (4) : 1529-1544. doi: 10.3934/era.2020080 |
[13] |
Mudassar Imran, Youssef Raffoul, Muhammad Usman, Chi Zhang. A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 691-705. doi: 10.3934/dcdss.2018043 |
[14] |
Peng Gao. Null controllability with constraints on the state for the 1-D Kuramoto-Sivashinsky equation. Evolution Equations and Control Theory, 2015, 4 (3) : 281-296. doi: 10.3934/eect.2015.4.281 |
[15] |
Fred C. Pinto. Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 117-136. doi: 10.3934/dcds.1999.5.117 |
[16] |
David Massatt. On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2021305 |
[17] |
Ralf W. Wittenberg. Optimal parameter-dependent bounds for Kuramoto-Sivashinsky-type equations. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 5325-5357. doi: 10.3934/dcds.2014.34.5325 |
[18] |
Seung-Yeal Ha, Javier Morales, Yinglong Zhang. Kuramoto order parameters and phase concentration for the Kuramoto-Sakaguchi equation with frustration. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2579-2612. doi: 10.3934/cpaa.2021013 |
[19] |
Yuqian Zhou, Qian Liu. Reduction and bifurcation of traveling waves of the KdV-Burgers-Kuramoto equation. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 2057-2071. doi: 10.3934/dcdsb.2016036 |
[20] |
Seung-Yeal Ha, Hansol Park, Yinglong Zhang. Nonlinear stability of stationary solutions to the Kuramoto-Sakaguchi equation with frustration. Networks and Heterogeneous Media, 2020, 15 (3) : 427-461. doi: 10.3934/nhm.2020026 |
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