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Preface
On Lyapunov stability of linearised Saint-Venant equations for a sloping channel
1. | Center for Systems Engineering and Applied Mechanics (CESAME), Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve |
2. | Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Institut Universitaire de France, 175, Rue du Chevaleret, 75013 Paris, France |
3. | Centre de Robotique (CAOR), Ecole nationale supérieure des mines de Paris, 60, Boulevard Saint Michel, 75272 Paris Cedex 06 |
[1] |
Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie, Mohammed Seaid. Multilayer Saint-Venant equations over movable beds. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 917-934. doi: 10.3934/dcdsb.2011.15.917 |
[2] |
E. Audusse. A multilayer Saint-Venant model: Derivation and numerical validation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 189-214. doi: 10.3934/dcdsb.2005.5.189 |
[3] |
Hassen Arfaoui, Faker Ben Belgacem, Henda El Fekih, Jean-Pierre Raymond. Boundary stabilizability of the linearized viscous Saint-Venant system. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 491-511. doi: 10.3934/dcdsb.2011.15.491 |
[4] |
Jean-Frédéric Gerbeau, Benoit Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 89-102. doi: 10.3934/dcdsb.2001.1.89 |
[5] |
Marie-Odile Bristeau, Jacques Sainte-Marie. Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 733-759. doi: 10.3934/dcdsb.2008.10.733 |
[6] |
Luis Barreira, Claudia Valls. Stability of nonautonomous equations and Lyapunov functions. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2631-2650. doi: 10.3934/dcds.2013.33.2631 |
[7] |
Feng Wang, José Ángel Cid, Mirosława Zima. Lyapunov stability for regular equations and applications to the Liebau phenomenon. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4657-4674. doi: 10.3934/dcds.2018204 |
[8] |
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks and Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007 |
[9] |
Carlos Arnoldo Morales, M. J. Pacifico. Lyapunov stability of $\omega$-limit sets. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 671-674. doi: 10.3934/dcds.2002.8.671 |
[10] |
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems and Imaging, 2016, 10 (4) : 869-898. doi: 10.3934/ipi.2016025 |
[11] |
Jean Ginibre, Giorgio Velo. Modified wave operators without loss of regularity for some long range Hartree equations. II. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1357-1376. doi: 10.3934/cpaa.2015.14.1357 |
[12] |
Mohamed Assellaou, Olivier Bokanowski, Hasnaa Zidani. Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 3933-3964. doi: 10.3934/dcds.2015.35.3933 |
[13] |
Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001 |
[14] |
Dongyi Liu, Genqi Xu. Input-output $ L^2 $-well-posedness, regularity and Lyapunov stability of string equations on networks. Networks and Heterogeneous Media, 2022 doi: 10.3934/nhm.2022007 |
[15] |
Jifeng Chu, Meirong Zhang. Rotation numbers and Lyapunov stability of elliptic periodic solutions. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1071-1094. doi: 10.3934/dcds.2008.21.1071 |
[16] |
Sigurdur Freyr Hafstein. A constructive converse Lyapunov theorem on exponential stability. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 657-678. doi: 10.3934/dcds.2004.10.657 |
[17] |
Jifeng Chu, Jinzhi Lei, Meirong Zhang. Lyapunov stability for conservative systems with lower degrees of freedom. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 423-443. doi: 10.3934/dcdsb.2011.16.423 |
[18] |
Georges Bastin, B. Haut, Jean-Michel Coron, Brigitte d'Andréa-Novel. Lyapunov stability analysis of networks of scalar conservation laws. Networks and Heterogeneous Media, 2007, 2 (4) : 751-759. doi: 10.3934/nhm.2007.2.751 |
[19] |
Volodymyr Pichkur. On practical stability of differential inclusions using Lyapunov functions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (5) : 1977-1986. doi: 10.3934/dcdsb.2017116 |
[20] |
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems and Imaging, 2013, 7 (2) : 307-340. doi: 10.3934/ipi.2013.7.307 |
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