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A multilayer Saint-Venant model: Derivation and numerical validation
Approximation of attractors of nonautonomous dynamical systems
1. | Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany, Germany |
2. | Department of Mathematics, University of Frankfurt, D-60325 Frankfurt, Germany |
[1] |
Chunqiu Li, Desheng Li, Xuewei Ju. On the forward dynamical behavior of nonautonomous systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 473-487. doi: 10.3934/dcdsb.2019190 |
[2] |
Yejuan Wang, Chengkui Zhong, Shengfan Zhou. Pullback attractors of nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems, 2006, 16 (3) : 587-614. doi: 10.3934/dcds.2006.16.587 |
[3] |
Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 579-596. doi: 10.3934/dcds.2006.15.579 |
[4] |
Hongyong Cui, Peter E. Kloeden, Meihua Yang. Forward omega limit sets of nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1103-1114. doi: 10.3934/dcdss.2020065 |
[5] |
Linfang Liu, Xianlong Fu, Yuncheng You. Pullback attractor in $H^{1}$ for nonautonomous stochastic reaction-diffusion equations on $\mathbb{R}^n$. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3629-3651. doi: 10.3934/dcdsb.2017143 |
[6] |
Yangrong Li, Lianbing She, Jinyan Yin. Longtime robustness and semi-uniform compactness of a pullback attractor via nonautonomous PDE. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1535-1557. doi: 10.3934/dcdsb.2018058 |
[7] |
Christian Pötzsche. Nonautonomous continuation of bounded solutions. Communications on Pure and Applied Analysis, 2011, 10 (3) : 937-961. doi: 10.3934/cpaa.2011.10.937 |
[8] |
Arne Ogrowsky, Björn Schmalfuss. Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1663-1681. doi: 10.3934/dcdsb.2013.18.1663 |
[9] |
Xiaoying Han, Peter E. Kloeden. Pullback and forward dynamics of nonautonomous Laplacian lattice systems on weighted spaces. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021143 |
[10] |
David Julitz. Numerical approximation of atmospheric-ocean models with subdivision algorithm. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 429-447. doi: 10.3934/dcds.2007.18.429 |
[11] |
Matteo Franca, Russell Johnson, Victor Muñoz-Villarragut. On the nonautonomous Hopf bifurcation problem. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1119-1148. doi: 10.3934/dcdss.2016045 |
[12] |
Xuewei Ju, Desheng Li, Jinqiao Duan. Forward attraction of pullback attractors and synchronizing behavior of gradient-like systems with nonautonomous perturbations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1175-1197. doi: 10.3934/dcdsb.2019011 |
[13] |
Peter E. Kloeden. Asymptotic invariance and the discretisation of nonautonomous forward attracting sets. Journal of Computational Dynamics, 2016, 3 (2) : 179-189. doi: 10.3934/jcd.2016009 |
[14] |
Wan-Tong Li, Bin-Guo Wang. Attractor minimal sets for nonautonomous type-K competitive and semi-convex delay differential equations with applications. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 589-611. doi: 10.3934/dcds.2009.24.589 |
[15] |
Mustapha Yebdri. Existence of $ \mathcal{D}- $pullback attractor for an infinite dimensional dynamical system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 167-198. doi: 10.3934/dcdsb.2021036 |
[16] |
Björn Schmalfuss. Attractors for nonautonomous and random dynamical systems perturbed by impulses. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 727-744. doi: 10.3934/dcds.2003.9.727 |
[17] |
David Cheban. Global attractors of nonautonomous quasihomogeneous dynamical systems. Conference Publications, 2001, 2001 (Special) : 96-101. doi: 10.3934/proc.2001.2001.96 |
[18] |
Yonghai Wang, Chengkui Zhong. Upper semicontinuity of pullback attractors for nonautonomous Kirchhoff wave models. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3189-3209. doi: 10.3934/dcds.2013.33.3189 |
[19] |
Jianhua Huang, Wenxian Shen. Pullback attractors for nonautonomous and random parabolic equations on non-smooth domains. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 855-882. doi: 10.3934/dcds.2009.24.855 |
[20] |
Christian Pötzsche. Nonautonomous bifurcation of bounded solutions II: A Shovel-Bifurcation pattern. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 941-973. doi: 10.3934/dcds.2011.31.941 |
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