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Stability of solitary-wave solutions to the Hirota-Satsuma equation
A fully nonlinear equation for the flame front in a quasi-steady combustion model
1. | Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 33405 Talence Cedex |
2. | Faculty of Sciences – Mathematics and Computer Science division, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081HV Amsterdam |
3. | Dipartimento di Matematica, Università degli Studi di Parma, Viale G. P. Usberti 53/A, 43124 Parma, Italy |
4. | School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel |
[1] |
Fred C. Pinto. Nonlinear stability and dynamical properties for a Kuramoto-Sivashinsky equation in space dimension two. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 117-136. doi: 10.3934/dcds.1999.5.117 |
[2] |
Kiah Wah Ong. Dynamic transitions of generalized Kuramoto-Sivashinsky equation. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1225-1236. doi: 10.3934/dcdsb.2016.21.1225 |
[3] |
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 |
[4] |
Jared C. Bronski, Razvan C. Fetecau, Thomas N. Gambill. A note on a non-local Kuramoto-Sivashinsky equation. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 701-707. doi: 10.3934/dcds.2007.18.701 |
[5] |
Eduardo Cerpa. Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation. Communications on Pure & 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 & Continuous Dynamical Systems - A, 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 & 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 & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 555-580. doi: 10.3934/dcdsb.2008.9.555 |
[10] |
Peng Gao. Averaging principle for stochastic Kuramoto-Sivashinsky equation with a fast oscillation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5649-5684. doi: 10.3934/dcds.2018247 |
[11] |
Peng Gao. Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation. Evolution Equations & Control Theory, 2020, 9 (1) : 181-191. doi: 10.3934/eect.2020002 |
[12] |
Ildoo Kim. An $L_p$-Lipschitz theory for parabolic equations with time measurable pseudo-differential operators. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2751-2771. doi: 10.3934/cpaa.2018130 |
[13] |
Lanzhe Liu. Mean oscillation and boundedness of Toeplitz Type operators associated to pseudo-differential operators. Communications on Pure & Applied Analysis, 2015, 14 (2) : 627-636. doi: 10.3934/cpaa.2015.14.627 |
[14] |
Aslihan Demirkaya. The existence of a global attractor for a Kuramoto-Sivashinsky type equation in 2D. Conference Publications, 2009, 2009 (Special) : 198-207. doi: 10.3934/proc.2009.2009.198 |
[15] |
Peng Gao. Null controllability with constraints on the state for the 1-D Kuramoto-Sivashinsky equation. Evolution Equations & Control Theory, 2015, 4 (3) : 281-296. doi: 10.3934/eect.2015.4.281 |
[16] |
JIAO CHEN, WEI DAI, GUOZHEN LU. $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators. Communications on Pure & Applied Analysis, 2017, 16 (3) : 883-898. doi: 10.3934/cpaa.2017042 |
[17] |
Ralf W. Wittenberg. Optimal parameter-dependent bounds for Kuramoto-Sivashinsky-type equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (12) : 5325-5357. doi: 10.3934/dcds.2014.34.5325 |
[18] |
Feliz Minhós. Periodic solutions for some fully nonlinear fourth order differential equations. Conference Publications, 2011, 2011 (Special) : 1068-1077. doi: 10.3934/proc.2011.2011.1068 |
[19] |
Isabeau Birindelli, Stefania Patrizi. A Neumann eigenvalue problem for fully nonlinear operators. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 845-863. doi: 10.3934/dcds.2010.28.845 |
[20] |
Isabeau Birindelli, Francoise Demengel. The dirichlet problem for singluar fully nonlinear operators. Conference Publications, 2007, 2007 (Special) : 110-121. doi: 10.3934/proc.2007.2007.110 |
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