Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain
From MaRDI portal
Publication:3440246
DOI10.1137/050631409zbMath1116.35108OpenAlexW2026967759MaRDI QIDQ3440246
Publication date: 22 May 2007
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/fe3be3b3053386e981f79c6c74ec387a608d7912
Stabilization of systems by feedback (93D15) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53)
Related Items (69)
Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws ⋮ Recurrent solutions of the Korteweg-de Vries equation with boundary force ⋮ Control and stabilization of the Rosenau equation posed on a periodic domain ⋮ On the stabilization for the high-order Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations with localized damping ⋮ On the semi-global stabilizability of the Korteweg-de Vries Equationviamodel predictive control ⋮ Recurrent solutions of the derivative Ginzburg–Landau equation with boundary forces ⋮ Center manifold for the third-order nonlinear Schrödinger equation with critical lengths ⋮ Robustness of exponential attractors for damped Korteweg-de Vries equations ⋮ Global Carleman estimate for the Kawahara equation and its applications ⋮ GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG–DE VRIES EQUATION ⋮ Bang-bang property for time optimal control of the Korteweg-de Vries-Burgers equation ⋮ Global Stabilization of a Korteweg--De Vries Equation With Saturating Distributed Control ⋮ ISS Lyapunov Strictification via Observer Design and Integral Action Control for a Korteweg–de Vries Equation ⋮ Control of a Boussinesq system of KdV–KdV type on a bounded interval ⋮ Stabilization of the Gear-Grimshaw system with weak damping ⋮ Unique continuation property for the Zakharov-Kuznetsov equation ⋮ Decay of solutions to damped Korteweg-de Vries type equation ⋮ CONTROLLABILITY OF THE KORTEWEG-DE VRIES-BURGERS EQUATION ⋮ Control of a Korteweg-de Vries equation: a tutorial ⋮ Energy decay for the modified Kawahara equation posed in a bounded domain ⋮ Carleman estimates for forward and backward stochastic fourth order Schrödinger equations and their applications ⋮ Global well-posedness and exponential decay rates for a KdV-Burgers equation with indefinite damping ⋮ Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right ⋮ Control and stabilization of the Korteweg-de Vries equation: recent progresses ⋮ Stabilization of a Boussinesq system of KdV-KdV type ⋮ Exponential decay for the linear KdV with a rough localized damping ⋮ Carleman estimates and unique continuation property for 1-D viscous Camassa-Holm equation ⋮ Uniform stabilization of a nonlinear dispersive system ⋮ Cone-bounded feedback laws for \(m\)-dissipative operators on Hilbert spaces ⋮ Output feedback stabilization of the Korteweg-de Vries equation ⋮ Distributed control of the generalized Korteweg-de Vries-Burgers equation ⋮ Null controllability with constraints on the state for the Korteweg-de Vries equation ⋮ Averaging principle for the Schrödinger equations ⋮ Discussion on: ``Adaptive boundary control of the forced generalized Korteweg-de Vries-Burgers equation ⋮ On the well-posedness and asymptotic behavior of a nonlinear dispersive system in weighted spaces ⋮ Pontryagin's maximum principle for optimal boundary control of a generalised Korteweg–de Vries equation ⋮ Controllability problems for the Korteweg-de Vries equation with integral overdetermination ⋮ Stability properties of a higher order scheme for a GKdV-4 equation modelling surface water waves ⋮ Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain ⋮ A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem ⋮ Initial-boundary value problems for generalized dispersive equations of higher orders posed on bounded intervals ⋮ Averaging principle for stochastic Korteweg-de Vries equation ⋮ On the stabilization and controllability for a third order linear equation ⋮ Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients ⋮ Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping ⋮ Qualitative analysis of the dynamic for the nonlinear Korteweg-de Vries equation with a boundary memory ⋮ Recurrent solutions of the Schrödinger-KdV system with boundary forces ⋮ Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation ⋮ Well-posedness of a nonlinear boundary value problem for the Korteweg-de Vries equation on a bounded domain ⋮ A Korteweg-de Vries type of fifth-order equations on a finite domain with point dissipation ⋮ On the controllability and stabilization of the linearized Benjamin equation on a periodic domain ⋮ Asymptotic behavior of the Korteweg-de Vries equation posed in a quarter plane ⋮ On the controllability and stabilization of the Benjamin equation on a periodic domain ⋮ Decay for the nonlinear KdV equations at critical lengths ⋮ A qualitative study and numerical simulations for a time-delayed dispersive equation ⋮ Stabilization of the Kawahara equation with localized damping ⋮ Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation ⋮ Exact boundary controllability of the nonlinear Schrödinger equation ⋮ Boosting the decay of solutions of the linearised Korteweg-de Vries–Burgers equation to a predetermined rate from the boundary ⋮ Uniform stabilization of a class of coupled systems of KdV equations with localized damping ⋮ Exponential stability for the generalized Korteweg-de Vries equation in a finite interval with weak damping ⋮ A NEW UNIQUE CONTINUATION PROPERTY FOR THE KORTEWEG–DE VRIES EQUATION ⋮ Control and stabilization of the Benjamin-Ono equation on a periodic domain ⋮ Global Carleman estimate and its applications for a sixth-order equation related to thin solid films ⋮ Exponential stabilization of a linear Korteweg-de Vries equation with input saturation ⋮ Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain ⋮ On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping ⋮ Rapid exponential stabilisation of linear-KdV equation with long input delay on the left boundary ⋮ Exponential decay for a locally damped fifth-order equation posed on the line
This page was built for publication: Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain
