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Asymptotic stability of a nonlinear Korteweg–de Vries equation with critical lengths

Jixun Chu, Jean-Michel Coron and Peipei Shang
Journal of Differential Equations 259 (8) 4045 (2015)
DOI: 10.1016/j.jde.2015.05.010
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Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system

Lionel Rosier, Ademir Pazoto and Dugan Nina
Evolution Equations and Control Theory 2 (2) 379 (2013)
DOI: 10.3934/eect.2013.2.379
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Unique continuation and decay for the Korteweg-de Vries equation with localized damping

Ademir Fernando Pazoto
ESAIM: Control, Optimisation and Calculus of Variations 11 (3) 473 (2005)
DOI: 10.1051/cocv:2005015
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Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain

Lionel Rosier and Bing-Yu Zhang
SIAM Journal on Control and Optimization 45 (3) 927 (2006)
DOI: 10.1137/050631409
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Control and stabilization of the Korteweg-de Vries equation: recent progresses

Lionel Rosier and Bing-Yu Zhang
Journal of Systems Science and Complexity 22 (4) 647 (2009)
DOI: 10.1007/s11424-009-9194-2
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Rapid Stabilization for a Korteweg-de Vries Equation >From the Left Dirichlet Boundary Condition

Eduardo Cerpa and Jean-Michel Coron
IEEE Transactions on Automatic Control 58 (7) 1688 (2013)
DOI: 10.1109/TAC.2013.2241479
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On the observability of time-discrete conservative linear systems

Sylvain Ervedoza, Chuang Zheng and Enrique Zuazua
Journal of Functional Analysis 254 (12) 3037 (2008)
DOI: 10.1016/j.jfa.2008.03.005
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The Bang-bang principle of time optimal controls for the Kuramoto-Sivashinsky-KdV equation with internal control

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International Journal of Robust and Nonlinear Control 26 (8) 1667 (2016)
DOI: 10.1002/rnc.3373
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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)
DOI: 10.1016/j.sysconle.2016.09.012
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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)
DOI: 10.1016/j.cam.2013.09.045
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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)
DOI: 10.1137/S0363012997327501
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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)
DOI: 10.1137/070709578
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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)
DOI: 10.1080/00036811.2015.1080247
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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)
DOI: 10.1016/j.anihpc.2007.11.003
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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)
DOI: 10.1016/j.anihpc.2009.01.010
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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)
DOI: 10.1016/j.anihpc.2013.08.003
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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)
DOI: 10.1016/j.anihpc.2020.12.004
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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)
DOI: 10.1016/j.na.2019.111646
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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)
DOI: 10.1137/16M1061837
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Uniform stabilization of a nonlinear dispersive system

A. Pazoto and G. Souza
Quarterly of Applied Mathematics 72 (1) 193 (2013)
DOI: 10.1090/S0033-569X-2013-01343-1
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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)
DOI: 10.1007/s11071-007-9222-5
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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)
DOI: 10.1002/mma.847
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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)
DOI: 10.1109/TAC.2018.2849564
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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)
DOI: 10.1007/978-1-4614-1806-1_8
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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

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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)
DOI: 10.1017/S0013091514000248
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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)
DOI: 10.1137/17M1115253
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Analysis, Probability, Applications, and Computation

Andrei V. Faminskii
Trends in Mathematics, Analysis, Probability, Applications, and Computation 939 305 (2019)
DOI: 10.1007/978-3-030-04459-6_29
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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)
DOI: 10.1619/fesi.63.293
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Control and stabilization of the Benjamin-Ono equation on a periodic domain

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Transactions of the American Mathematical Society 367 (7) 4595 (2015)
DOI: 10.1090/S0002-9947-2015-06086-3
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Exponential stabilization of an ODE–linear KdV cascaded system with boundary input delay

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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)
DOI: 10.1016/j.jmaa.2020.124848
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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)
DOI: 10.1016/j.jde.2020.11.025
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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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On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback

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Mathematical Control & Related Fields (2021)
DOI: 10.3934/mcrf.2021039
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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)
DOI: 10.1016/j.cnsns.2020.105669
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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)
DOI: 10.1007/s11854-018-0074-3
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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

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Journal of Applied Analysis & Computation 10 (2) 411 (2020)
DOI: 10.11948/20180018
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Null-controllability of linear hyperbolic systems in one dimensional space

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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

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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)
DOI: 10.1016/j.na.2021.112267
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Exponential stabilization of a linear Korteweg-de Vries equation with input saturation

Ahmat Mahamat Taboye and Mohamed Laabissi
Evolution Equations & Control Theory (2021)
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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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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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)
DOI: 10.1016/j.camwa.2021.05.001
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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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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)
DOI: 10.1515/anona-2016-0097
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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 & Control Theory (2021)
DOI: 10.3934/eect.2021062
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Local well-posedness of the coupled KdV-KdV systems on $ \mathbb{R} $

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Evolution Equations & Control Theory (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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Delayed stabilization of the Korteweg–de Vries equation on a star-shaped network

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Mathematics of Control, Signals, and Systems (2022)
DOI: 10.1007/s00498-022-00319-0
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Exponential decay for the KdV equation on ℝ with new localized dampings

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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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Modified Zakharov-Kuznetsov Equation Posed on a Half-Strip

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Applied Mathematics & Optimization 85 (3) (2022)
DOI: 10.1007/s00245-022-09877-w
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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

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Mathematical Methods in the Applied Sciences (2022)
DOI: 10.1002/mma.8369
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