Control of the surface of a fluid by a wavemaker
ESAIM: COCV, 10 3 (2004) 346-380
Published online: 2004-06-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Local controllability of the Korteweg-de Vries equation with the right Dirichlet control
Hoai-Minh NguyenJournal of Differential Equations 435 113235 (2025)
https://doi.org/10.1016/j.jde.2025.113235
Null controllability of KdV equation in a star-shaped network
Hugo ParadaEvolution Equations and Control Theory (2024)
https://doi.org/10.3934/eect.2024003
An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation
Nicolás Carreño and Cristóbal LoyolaJournal of Evolution Equations 23 (3) (2023)
https://doi.org/10.1007/s00028-023-00907-w
Global Approximate Controllability of the Korteweg-de Vries Equation by a Finite-Dimensional Force
Mo ChenApplied Mathematics & Optimization 87 (1) (2023)
https://doi.org/10.1007/s00245-022-09924-6
Global Well-Posedness of the KdV Equation on a Star-Shaped Network and Stabilization by Saturated Controllers
Hugo Parada, Emmanuelle Crépeau and Christophe PrieurSIAM Journal on Control and Optimization 60 (4) 2268 (2022)
https://doi.org/10.1137/21M1434581
Initial-boundary value problem of fifth-order Korteweg-de Vries equation posed on half line with nonlinear boundary values
Xiangqing Zhao, Chengqiang Wang and Jifeng BaoOpen Mathematics 20 (1) 529 (2022)
https://doi.org/10.1515/math-2022-0040
Output Feedback Control of a Cascade System of Linear Korteweg--de Vries Equations
Constantinos Kitsos, Eduardo Cerpa, Gildas Besançon and Christophe PrieurSIAM Journal on Control and Optimization 59 (4) 2955 (2021)
https://doi.org/10.1137/20M1350066
Qualitative Analysis of the Dynamic for the Nonlinear Korteweg–de Vries Equation with a Boundary Memory
Boumediène ChentoufQualitative Theory of Dynamical Systems 20 (2) (2021)
https://doi.org/10.1007/s12346-021-00472-y
Weak damping for the Korteweg-de Vries equation
Roberto de A. Capistrano FilhoElectronic Journal of Qualitative Theory of Differential Equations (43) 1 (2021)
https://doi.org/10.14232/ejqtde.2021.1.43
Local exact controllability to the trajectories of the Korteweg–de Vries–Burgers equation on a bounded domain with mixed boundary conditions
Eduardo Cerpa, Cristhian Montoya and Bingyu ZhangJournal of Differential Equations 268 (9) 4945 (2020)
https://doi.org/10.1016/j.jde.2019.10.043
BOUNDARY CONTROLLABILITY FOR THE TIME-FRACTIONAL NONLINEAR KORTEWEG-DE VRIES (KDV) EQUATION
Jingqun Wang and Lixin TianJournal of Applied Analysis & Computation 10 (2) 411 (2020)
https://doi.org/10.11948/20180018
Initial boundary value problem for Korteweg–de Vries equation: a review and open problems
Roberto A. Capistrano-Filho, Shu-Ming Sun and Bing-Yu ZhangSão Paulo Journal of Mathematical Sciences 13 (2) 402 (2019)
https://doi.org/10.1007/s40863-019-00120-z
Controllability Problems for the Korteweg–de Vries Equation with Integral Overdetermination
A. V. FaminskiiDifferential Equations 55 (1) 126 (2019)
https://doi.org/10.1134/S0012266119010130
Trajectory Controllability of the Nonlinear Systems Governed by Fractional Differential Equations
M. Muslim and Raju K. GeorgeDifferential Equations and Dynamical Systems 27 (4) 529 (2019)
https://doi.org/10.1007/s12591-016-0292-z
Control Problems with an Integral Condition for Korteweg–de Vries Equation on Unbounded Domains
Andrei V. FaminskiiJournal of Optimization Theory and Applications 180 (1) 290 (2019)
https://doi.org/10.1007/s10957-018-1360-z
Exact Controllability of a Linear Korteweg--de Vries Equation by the Flatness Approach
Philippe Martin, Ivonne Rivas, Lionel Rosier and Pierre RouchonSIAM Journal on Control and Optimization 57 (4) 2467 (2019)
https://doi.org/10.1137/18M1181390
Null Controllability of a Linearized Korteweg--de Vries Equation by Backstepping Approach
S. XiangSIAM Journal on Control and Optimization 57 (2) 1493 (2019)
https://doi.org/10.1137/17M1115253
Uniform null controllability of a linear KdV equation using two controls
N. Carreño and S. GuerreroJournal of Mathematical Analysis and Applications 457 (1) 922 (2018)
https://doi.org/10.1016/j.jmaa.2017.08.039
Small-time local stabilization for a Korteweg–de Vries equation
Shengquan XiangSystems & Control Letters 111 64 (2018)
https://doi.org/10.1016/j.sysconle.2017.11.003
On the semi-global stabilizability of the Korteweg-de Vries Equation via model predictive control
Behzad Azmi, Anne-Céline Boulanger and Karl KunischESAIM: Control, Optimisation and Calculus of Variations 24 (1) 237 (2018)
https://doi.org/10.1051/cocv/2017001
Bang–Bang Property for Time Optimal Control of the Korteweg-de Vries-Burgers Equation
Mo ChenApplied Mathematics & Optimization 76 (2) 399 (2017)
https://doi.org/10.1007/s00245-016-9355-3
Local exponential stabilization for a class of Korteweg–de Vries equations by means of time-varying feedback laws
Jean-Michel Coron, Ivonne Rivas and Shengquan XiangAnalysis & PDE 10 (5) 1089 (2017)
https://doi.org/10.2140/apde.2017.10.1089
Neumann Boundary Controllability of the Korteweg--de Vries Equation on a Bounded Domain
Miguel Andres Caicedo, Roberto Capistrano Filho and Bing-Yu ZhangSIAM Journal on Control and Optimization 55 (6) 3503 (2017)
https://doi.org/10.1137/15M103755X
Controllability Aspects of the Korteweg-de Vries Burgers Equation on Unbounded Domains
F.A. GallegoJournal of Mathematical Analysis and Applications (2017)
https://doi.org/10.1016/j.jmaa.2017.12.031
Well-posedness of a nonlinear boundary value problem for the Korteweg–de Vries equation on a bounded domain
Miguel Andres Caicedo and Bing-Yu ZhangJournal of Mathematical Analysis and Applications 448 (2) 797 (2017)
https://doi.org/10.1016/j.jmaa.2016.11.032
Optimal distributed control of the Kuramoto–Sivashinsky equation with pointwise state and mixed control-state constraints
Peng GaoIMA Journal of Mathematical Control and Information 33 (3) 791 (2016)
https://doi.org/10.1093/imamci/dnv010
Lagrangian Controllability of the 1-Dimensional Korteweg--de Vries Equation
Ludovick GagnonSIAM Journal on Control and Optimization 54 (6) 3152 (2016)
https://doi.org/10.1137/140964783
Asymptotic stability of a nonlinear Korteweg–de Vries equation with critical lengths
Jixun Chu, Jean-Michel Coron and Peipei ShangJournal of Differential Equations 259 (8) 4045 (2015)
https://doi.org/10.1016/j.jde.2015.05.010
Generation of 2D water waves by moving bottom disturbances
Hayk Nersisyan, Denys Dutykh and Enrique ZuazuaIMA Journal of Applied Mathematics 80 (4) 1235 (2015)
https://doi.org/10.1093/imamat/hxu051
Local Exact Controllability of a One-Dimensional Nonlinear Schrödinger Equation
Karine Beauchard, Horst Lange and Holger TeismannSIAM Journal on Control and Optimization 53 (5) 2781 (2015)
https://doi.org/10.1137/140951618
Internal controllability of the korteweg–de vries equation on a bounded domain
Roberto A. Capistrano–Filho, Ademir F. Pazoto and Lionel RosierESAIM: Control, Optimisation and Calculus of Variations 21 (4) 1076 (2015)
https://doi.org/10.1051/cocv/2014059
Applied Mathematics in Tunisia
Hajer Dbebria and Ali SalemSpringer Proceedings in Mathematics & Statistics, Applied Mathematics in Tunisia 131 293 (2015)
https://doi.org/10.1007/978-3-319-18041-0_19
On the non-uniform null controllability of a linear KdV equation
N. Carreño and S. GuerreroAsymptotic Analysis 94 (1-2) 33 (2015)
https://doi.org/10.3233/ASY-151300
A NEW UNIQUE CONTINUATION PROPERTY FOR THE KORTEWEG–DE VRIES EQUATION
MO CHEN and PENG GAOBulletin of the Australian Mathematical Society 90 (1) 90 (2014)
https://doi.org/10.1017/S000497271300110X
Control of a Korteweg-de Vries equation: A tutorial
Eduardo CerpaMathematical Control & Related Fields 4 (1) 45 (2014)
https://doi.org/10.3934/mcrf.2014.4.45
Local rapid stabilization for a Korteweg–de Vries equation with a Neumann boundary control on the right
Jean-Michel Coron and Qi LüJournal de Mathématiques Pures et Appliquées 102 (6) 1080 (2014)
https://doi.org/10.1016/j.matpur.2014.03.004
On the Cost of Fast Controls for Some Families of Dispersive or Parabolic Equations in One Space Dimension
Pierre LissySIAM Journal on Control and Optimization 52 (4) 2651 (2014)
https://doi.org/10.1137/140951746
Null controllability of a linear KdV equation on an interval with special boundary conditions
Jean-Philippe GuilleronMathematics of Control, Signals, and Systems 26 (3) 375 (2014)
https://doi.org/10.1007/s00498-013-0122-6
Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system
Dugan Nina, Ademir Fernando Pazoto and Lionel RosierEvolution Equations & Control Theory 2 (2) 379 (2013)
https://doi.org/10.3934/eect.2013.2.379
Uniform stabilization of a nonlinear dispersive system
A. Pazoto and G. SouzaQuarterly of Applied Mathematics 72 (1) 193 (2013)
https://doi.org/10.1090/S0033-569X-2013-01343-1
Boundary Controllability of the Korteweg--de Vries Equation on a Bounded Domain
Eduardo Cerpa, Ivonne Rivas and Bing-Yu ZhangSIAM Journal on Control and Optimization 51 (4) 2976 (2013)
https://doi.org/10.1137/120891721
Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition
Eduardo Cerpa and Jean-Michel CoronIEEE Transactions on Automatic Control 58 (7) 1688 (2013)
https://doi.org/10.1109/TAC.2013.2241479
Global stabilization of a coupled system of two generalized Korteweg-de Vries type equations posed on a finite domain
Dugan Nina, Ademir Fernando Pazoto and Lionel RosierMathematical Control & Related Fields 1 (3) 353 (2011)
https://doi.org/10.3934/mcrf.2011.1.353
Pontryagin's maximum principle for optimal boundary control of a generalised Korteweg–de Vries equation
Bing SunInternational Journal of Systems Science 41 (6) 699 (2010)
https://doi.org/10.1080/00207720903151300
Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain
Camille Laurent, Lionel Rosier and Bing-Yu ZhangCommunications in Partial Differential Equations 35 (4) 707 (2010)
https://doi.org/10.1080/03605300903585336
Discussion on: “Adaptive Boundary Control of the Forced Generalized Korteweg-de Vries-Burgers Equation”
Emmanuelle Crépeau and Christophe PrieurEuropean Journal of Control 16 (1) 85 (2010)
https://doi.org/10.1016/S0947-3580(10)70625-7
Controllability of the Korteweg–de Vries equation from the right Dirichlet boundary condition
O. Glass and S. GuerreroSystems & Control Letters 59 (7) 390 (2010)
https://doi.org/10.1016/j.sysconle.2010.05.001
Control and stabilization of the Korteweg-de Vries equation: recent progresses
Lionel Rosier and Bing-Yu ZhangJournal of Systems Science and Complexity 22 (4) 647 (2009)
https://doi.org/10.1007/s11424-009-9194-2
GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG–DE VRIES EQUATION
MARIANNE CHAPOULYCommunications in Contemporary Mathematics 11 (03) 495 (2009)
https://doi.org/10.1142/S0219199709003454
Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain
Eduardo Cerpa and Emmanuelle CrépeauAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 26 (2) 457 (2009)
https://doi.org/10.1016/j.anihpc.2007.11.003
On the controllability of the fifth-order Korteweg–de Vries equation
O. Glass and S. GuerreroAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 26 (6) 2181 (2009)
https://doi.org/10.1016/j.anihpc.2009.01.010
UNIFORM CONTROLLABILITY OF A TRANSPORT EQUATION IN ZERO DIFFUSION–DISPERSION LIMIT
OLIVIER GLASS and SERGIO GUERREROMathematical Models and Methods in Applied Sciences 19 (09) 1567 (2009)
https://doi.org/10.1142/S0218202509003899
Controllability and asymptotic stabilization of the Camassa–Holm equation
Olivier GlassJournal of Differential Equations 245 (6) 1584 (2008)
https://doi.org/10.1016/j.jde.2008.06.016
On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping
F. Linares and A. PazotoProceedings of the American Mathematical Society 135 (5) 1515 (2007)
https://doi.org/10.1090/S0002-9939-07-08810-7
Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain
Lionel Rosier and Bing-Yu ZhangSIAM Journal on Control and Optimization 45 (3) 927 (2006)
https://doi.org/10.1137/050631409