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Cited article:
L. Rosier
ESAIM: COCV, 2 (1997) 33-55
Published online: 2002-08-15
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Journal of Functional Analysis 254 (12) 3037 (2008)
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The Bang-bang principle of time optimal controls for the Kuramoto-Sivashinsky-KdV equation with internal control
Jiashan Zheng
International Journal of Robust and Nonlinear Control 26 (8) 1667 (2016)
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Exact boundary controllability of the Korteweg–de Vries equation with a piecewise constant main coefficient
Emmanuelle Crépeau
Systems & Control Letters 97 157 (2016)
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Numerical studies of the damped Korteweg–de Vries system
M.A. Rincon, F.S. Teixeira and I.F. Lopez
Journal of Computational and Applied Mathematics 259 294 (2014)
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Exact Boundary Controllability of the Korteweg--de Vries Equation
Bing-Yu Zhang
SIAM Journal on Control and Optimization 37 (2) 543 (1999)
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Local Exact Controllability and Stabilizability of the Nonlinear Schrödinger Equation on a Bounded Interval
Lionel Rosier and Bing-Yu Zhang
SIAM Journal on Control and Optimization 48 (2) 972 (2009)
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Global Stabilization of The Generalized Burgers-Korteweg-de Vries Equation by Boundary Control
Agus Hasan and Bjarne Foss
IFAC Proceedings Volumes 44 (1) 6771 (2011)
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Boundary Controllability of the Korteweg--de Vries Equation on a Bounded Domain
Eduardo Cerpa, Ivonne Rivas and Bing-Yu Zhang
SIAM Journal on Control and Optimization 51 (4) 2976 (2013)
DOI: 10.1137/120891721
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-Insensitizing controls for the linear stochastic Korteweg-de Vries equation
Peng Gao
Applicable Analysis 95 (9) 1919 (2016)
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Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain
Eduardo Cerpa and Emmanuelle Crépeau
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 26 (2) 457 (2009)
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On the controllability of the fifth-order Korteweg–de Vries equation
O. Glass and S. Guerrero
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 26 (6) 2181 (2009)
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Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping
M.M. Cavalcanti, V.N. Domingos Cavalcanti, V. Komornik and J.H. Rodrigues
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 31 (5) 1079 (2014)
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Boundary observability of gravity water waves
Thomas Alazard
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35 (3) 751 (2018)
DOI: 10.1016/j.anihpc.2017.07.006
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Output feedback stabilization of the linearized Korteweg–de Vries equation with right endpoint controllers
Ahmet Batal and Türker Özsarı
Automatica 109 108531 (2019)
DOI: 10.1016/j.automatica.2019.108531
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On the controllability and stabilization of the Benjamin equation on a periodic domain
M. Panthee and F. Vielma Leal
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 38 (5) 1605 (2021)
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Neumann Boundary Controllability of the Korteweg--de Vries Equation on a Bounded Domain
Miguel Andres Caicedo, Roberto Capistrano Filho and Bing-Yu Zhang
SIAM Journal on Control and Optimization 55 (6) 3503 (2017)
DOI: 10.1137/15M103755X
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Global Stabilization of a Korteweg--De Vries Equation With Saturating Distributed Control
Swann Marx, Eduardo Cerpa, Christophe Prieur and Vincent Andrieu
SIAM Journal on Control and Optimization 55 (3) 1452 (2017)
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Uniform stabilization of a nonlinear dispersive system
A. Pazoto and G. Souza
Quarterly of Applied Mathematics 72 (1) 193 (2013)
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Boundary control of the generalized Korteweg–de Vries–Burgers equation
Nejib Smaoui and Rasha H. Al-Jamal
Nonlinear Dynamics 51 (3) 439 (2008)
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On the uniform decay for the Korteweg–de Vries equation with weak damping
C. P. Massarolo, G. P. Menzala and A. F. Pazoto
Mathematical Methods in the Applied Sciences 30 (12) 1419 (2007)
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Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit
Olivier Glass and Sergio Guerrero
PAMM 7 (1) 1041601 (2007)
DOI: 10.1002/pamm.200701006
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Well-posedness of a nonlinear boundary value problem for the Korteweg–de Vries equation on a bounded domain
Miguel Andres Caicedo and Bing-Yu Zhang
Journal of Mathematical Analysis and Applications 448 (2) 797 (2017)
DOI: 10.1016/j.jmaa.2016.11.032
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Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping
A. F. Pazoto, M. Sepúlveda and O. Vera Villagrán
Numerische Mathematik 116 (2) 317 (2010)
DOI: 10.1007/s00211-010-0291-x
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Boundary feedback stabilization of the Korteweg–de Vries–Burgers equation posed on a finite interval
Chaohua Jia
Journal of Mathematical Analysis and Applications 444 (1) 624 (2016)
DOI: 10.1016/j.jmaa.2016.06.063
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Two approaches for the stabilization of the nonlinear KdV equation with boundary time-delay feedback
Emmanuelle Crepeau, Lucie Baudouin and Julie Valein
IEEE Transactions on Automatic Control 1 (2018)
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Internal controllability of the Kawahara equation on a bounded domain
Mo Chen
Nonlinear Analysis 185 356 (2019)
DOI: 10.1016/j.na.2019.03.016
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Mathematics of Complexity and Dynamical Systems
Olivier Glass
Mathematics of Complexity and Dynamical Systems 755 (2012)
DOI: 10.1007/978-1-4614-1806-1_46
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Mathematics of Complexity and Dynamical Systems
Lionel Rosier
Mathematics of Complexity and Dynamical Systems 395 (2012)
DOI: 10.1007/978-1-4614-1806-1_26
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Mathematics of Complexity and Dynamical Systems
Fatiha Alabau‐Boussouira and Piermarco Cannarsa
Mathematics of Complexity and Dynamical Systems 102 (2012)
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On the well-posedness and large-time behavior of higher order Boussinesq system
Roberto A Capistrano-Filho, Fernando A Gallego and Ademir F Pazoto
Nonlinearity 32 (5) 1852 (2019)
DOI: 10.1088/1361-6544/aafe34
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Pseudo-Backstepping and Its Application to the Control of Korteweg--de Vries Equation from the Right Endpoint on a Finite Domain
Türker Özsarı and Ahmet Batal
SIAM Journal on Control and Optimization 57 (2) 1255 (2019)
DOI: 10.1137/18M1211933
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Stabilization of Regular Solutions for the Zakharov-Kuznetsov Equation Posed on Bounded Rectangles and on a Strip
G. G. Doronin and N. A. Larkin
Proceedings of the Edinburgh Mathematical Society 58 (3) 661 (2015)
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Null Controllability of a Linearized Korteweg--de Vries Equation by Backstepping Approach
S. Xiang
SIAM Journal on Control and Optimization 57 (2) 1493 (2019)
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Analysis, Probability, Applications, and Computation
Andrei V. Faminskii
Trends in Mathematics, Analysis, Probability, Applications, and Computation 939 305 (2019)
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Wellposedness and Asymptotic Behavior of the Perturbed Nonlinear Schrödinger Equation with Kerr Law Nonlinearity and Localized Damping
Zaiyun Zhang, Zhenhai Liu and Mingbao Sun
Funkcialaj Ekvacioj 63 (3) 293 (2020)
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Exponential stabilization of an ODE–linear KdV cascaded system with boundary input delay
Habib Ayadi
IMA Journal of Mathematical Control and Information 37 (4) 1506 (2020)
DOI: 10.1093/imamci/dnaa022
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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 Zhang
Journal of Differential Equations 268 (9) 4945 (2020)
DOI: 10.1016/j.jde.2019.10.043
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Non-homogeneous initial-boundary-value problem of the fifth-order Korteweg-de Vries equation with a nonlinear dispersive term
Deqin Zhou
Journal of Mathematical Analysis and Applications 497 (1) 124848 (2021)
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Modified and subcritical Zakharov-Kuznetsov equations posed on rectangles
M. Castelli and G. Doronin
Journal of Differential Equations 275 554 (2021)
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Initial boundary value problem for Korteweg–de Vries equation: a review and open problems
Roberto A. Capistrano-Filho, Shu-Ming Sun and Bing-Yu Zhang
São Paulo Journal of Mathematical Sciences 13 (2) 402 (2019)
DOI: 10.1007/s40863-019-00120-z
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Non-homogeneous boundary value problems for some KdV-type equations on a finite interval: A numerical approach
Juan Carlos Muñoz Grajales
Communications in Nonlinear Science and Numerical Simulation 96 105669 (2021)
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Stabilization of a Boussinesq system with localized damping
Sorin Micu and Ademir F. Pazoto
Journal d'Analyse Mathématique 137 (1) 291 (2019)
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Modified Zakharov–Kuznetsov equation posed on a strip
M. Castelli and G. Doronin
Applicable Analysis 101 (2) 574 (2022)
DOI: 10.1080/00036811.2020.1754402
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BOUNDARY CONTROLLABILITY FOR THE TIME-FRACTIONAL NONLINEAR KORTEWEG-DE VRIES (KDV) EQUATION
Jingqun Wang and Lixin Tian
Journal of Applied Analysis & Computation 10 (2) 411 (2020)
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Null-controllability of linear hyperbolic systems in one dimensional space
Jean-Michel Coron and Hoai-Minh Nguyen
Systems & Control Letters 148 104851 (2021)
DOI: 10.1016/j.sysconle.2020.104851
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Supercritical Zakharov–Kuznetsov equation posed on bounded rectangles
M. Castelli and G. Doronin
Zeitschrift für angewandte Mathematik und Physik 72 (1) (2021)
DOI: 10.1007/s00033-020-01463-w
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On the controllability of a model system for long waves in nonlinear dispersive media
George J Bautista, Sorin Micu and Ademir F Pazoto
Nonlinearity 34 (2) 989 (2021)
DOI: 10.1088/1361-6544/abb453
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Well-posedness and controllability of Kawahara equation in weighted Sobolev spaces
Roberto de A. Capistrano-Filho and Milena Monique de S. Gomes
Nonlinear Analysis 207 112267 (2021)
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Exponential stabilization of a linear Korteweg-de Vries equation with input saturation
Ahmat Mahamat Taboye and Mohamed Laabissi
Evolution Equations and Control Theory 11 (5) 1519 (2022)
DOI: 10.3934/eect.2021052
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Exponential decay for the linear KdV with a rough localized damping
Ming Wang and Deqin Zhou
Applied Mathematics Letters 120 107264 (2021)
DOI: 10.1016/j.aml.2021.107264
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Eduardo Cerpa
1 (2013)
DOI: 10.1007/978-1-4471-5102-9_13-1
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Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation
Marcelo M. Cavalcanti, Wellington J. Corrêa, Andrei V. Faminskii, Mauricio A. Sepúlveda C. and Rodrigo Véjar-Asem
Computers & Mathematics with Applications 96 188 (2021)
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Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold
Shuxia Tang, Jixun Chu, Peipei Shang and Jean-Michel Coron
Advances in Nonlinear Analysis 7 (4) 497 (2018)
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Martin Gugat
69 (2015)
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Local well-posedness of the coupled KdV-KdV systems on $ \mathbb{R} $
Xin Yang and Bing-Yu Zhang
Evolution Equations and Control Theory 11 (5) 1829 (2022)
DOI: 10.3934/eect.2022002
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Well-posedness and stability results for the Korteweg–de Vries–Burgers and Kuramoto–Sivashinsky equations with infinite memory: A history approach
Boumediène Chentouf and Aissa Guesmia
Nonlinear Analysis: Real World Applications 65 103508 (2022)
DOI: 10.1016/j.nonrwa.2022.103508
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Local null controllability of a model system for strong interaction between internal solitary waves
Jon Asier Bárcena-Petisco, Sergio Guerrero and Ademir F. Pazoto
Communications in Contemporary Mathematics 24 (02) (2022)
DOI: 10.1142/S0219199721500036
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Stabilization results for delayed fifth-order KdV-type equation in a bounded domain
Roberto de A. Capistrano-Filho and Victor Hugo Gonzalez Martinez
Mathematical Control and Related Fields (2023)
DOI: 10.3934/mcrf.2023004
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Martin Gugat
1 (2015)
DOI: 10.1007/978-3-319-18890-4_1
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Martin Gugat
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DOI: 10.1007/978-3-319-18890-4_4
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Martin Gugat
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DOI: 10.1007/978-3-319-18890-4_2
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Martin Gugat
29 (2015)
DOI: 10.1007/978-3-319-18890-4_3
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Two stability results for the Kawahara equation with a time-delayed boundary control
Roberto de A. Capistrano-Filho, Boumediène Chentouf, Luan S. de Sousa and Victor H. Gonzalez Martinez
Zeitschrift für angewandte Mathematik und Physik 74 (1) (2023)
DOI: 10.1007/s00033-022-01897-4
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Rapid exponential stabilization of a Boussinesq system of KdV–KdV Type
Roberto de A. Capistrano–Filho, Eduardo Cerpa and Fernando A. Gallego
Communications in Contemporary Mathematics 25 (03) (2023)
DOI: 10.1142/S021919972150111X
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Identification of an unknown coefficient in KdV equation from final time measurement
Kumarasamy Sakthivel, Soundararajan Gnanavel, Alemdar Hasanov and Raju K. George
Journal of Inverse and Ill-posed Problems 24 (4) 469 (2016)
DOI: 10.1515/jiip-2016-0011
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On a multi-objective control problem for the Korteweg–de Vries equation
Islanita C. A. Albuquerque, Fágner D. Araruna and Maurício C. Santos
Calculus of Variations and Partial Differential Equations 62 (4) (2023)
DOI: 10.1007/s00526-023-02471-0
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Control and stabilization of the Benjamin-Ono equation on a periodic domain
Felipe Linares and Lionel Rosier
Transactions of the American Mathematical Society 367 (7) 4595 (2015)
DOI: 10.1090/S0002-9947-2015-06086-3
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Stability results for the KdV equation with time-varying delay
Hugo Parada, Chahnaz Timimoun and Julie Valein
Systems & Control Letters 177 105547 (2023)
DOI: 10.1016/j.sysconle.2023.105547
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Exponential decay for the KdV equation on ℝ with new localized dampings
Ming Wang and Deqin Zhou
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 1 (2022)
DOI: 10.1017/prm.2022.17
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Exact controllability and stabilization for a general internal wave system of Benjamin-Ono type
José R. Quintero and Alex M. Montes
Evolution Equations and Control Theory 11 (3) 681 (2022)
DOI: 10.3934/eect.2021021
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On the stabilization for the high-order Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations with localized damping
Roger P. de Moura, Ailton C. Nascimento and Gleison N. Santos
Evolution Equations and Control Theory 11 (3) 711 (2022)
DOI: 10.3934/eect.2021022
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On the global controllability of the 1-D Boussinesq equation
Chaker Jammazi and Souhila Loucif
Discrete and Continuous Dynamical Systems - S 15 (6) 1499 (2022)
DOI: 10.3934/dcdss.2022096
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Well‐posedness and exponential stability of the Kawahara equation with a time‐delayed localized damping
Boumediène Chentouf
Mathematical Methods in the Applied Sciences 45 (16) 10312 (2022)
DOI: 10.1002/mma.8369
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Modified Zakharov-Kuznetsov Equation Posed on a Half-Strip
M. Castelli, G. Doronin and M. V. Padilha
Applied Mathematics & Optimization 85 (3) (2022)
DOI: 10.1007/s00245-022-09877-w
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Decay for the nonlinear KdV equations at critical lengths
Hoai-Minh Nguyen
Journal of Differential Equations 295 249 (2021)
DOI: 10.1016/j.jde.2021.05.057
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Control results with overdetermination condition for higher order dispersive system
Roberto de A. Capistrano-Filho and Luan Soares de Sousa
Journal of Mathematical Analysis and Applications 506 (1) 125546 (2022)
DOI: 10.1016/j.jmaa.2021.125546
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Well-posedness and exponential decay estimates for a Korteweg–de Vries–Burgers equation with time-delay
Vilmos Komornik and Cristina Pignotti
Nonlinear Analysis 191 111646 (2020)
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On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback
Julie Valein
Mathematical Control and Related Fields 12 (3) 667 (2022)
DOI: 10.3934/mcrf.2021039
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On the control issues for higher-order nonlinear dispersive equations on the circle
Roberto de A. Capistrano–Filho, Chulkwang Kwak and Francisco J. Vielma Leal
Nonlinear Analysis: Real World Applications 68 103695 (2022)
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Olivier Glass
4804 (2009)
DOI: 10.1007/978-0-387-30440-3_284
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Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain
Francisco J. Vielma leal and Ademir Pastor
Evolution Equations and Control Theory 11 (5) 1745 (2022)
DOI: 10.3934/eect.2021062
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Delayed stabilization of the Korteweg–de Vries equation on a star-shaped network
Hugo Parada, Emmanuelle Crépeau and Christophe Prieur
Mathematics of Control, Signals, and Systems 34 (3) 559 (2022)
DOI: 10.1007/s00498-022-00319-0
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Global Well-Posedness of the KdV Equation on a Star-Shaped Network and Stabilization by Saturated Controllers
Hugo Parada, Emmanuelle Crépeau and Christophe Prieur
SIAM Journal on Control and Optimization 60 (4) 2268 (2022)
DOI: 10.1137/21M1434581
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A single bounded input‐feedback control to the generalized Korteweg–de Vries–Burgers–Kuramoto–Sivashinsky equation
Rasha Al Jamal and Nejib Smaoui
Mathematical Methods in the Applied Sciences 46 (2) 2222 (2023)
DOI: 10.1002/mma.8640
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Fatiha Alabau‐Boussouira and Piermarco Cannarsa
1485 (2009)
DOI: 10.1007/978-0-387-30440-3_97
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Asymptotic behavior of a linear higher-order BBM-system with damping
Oscar A. Sierra Fonseca and Ademir F. Pazoto
Zeitschrift für angewandte Mathematik und Physik 73 (6) (2022)
DOI: 10.1007/s00033-022-01861-2
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Boundary controllability and stabilizability of a coupled first-order hyperbolic-elliptic system
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DOI: 10.3934/eect.2022054
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On the exact controllability for the Benney-Luke equation in a bounded domain
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Evolution Equations and Control Theory (2022)
DOI: 10.3934/eect.2022052
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Global Approximate Controllability of the Korteweg-de Vries Equation by a Finite-Dimensional Force
Mo Chen
Applied Mathematics & Optimization 87 (1) (2023)
DOI: 10.1007/s00245-022-09924-6
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Asymptotic behavior of the Korteweg–de Vries equation posed in a quarter plane
F. Linares and A.F. Pazoto
Journal of Differential Equations 246 (4) 1342 (2009)
DOI: 10.1016/j.jde.2008.11.002
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