相关论文: Local controllability of the Korteweg-de Vries equ…

We investigate the local boundary controllability of the Korteweg-de Vries (KdV) equation with right Neumann boundary controls at critical lengths. We show that the KdV system is not locally null-controllable in small time for all critical…

This paper is devoted to the local null-controllability of the nonlinear KdV equation equipped the Dirichlet boundary conditions using the Neumann boundary control on the right. Rosier proved that this KdV system is small-time locally…

In this paper, we consider the small-time local controllability problem for the KdV system on an interval with a Neumann boundary control. In 1997, Rosier discovered that the linearized system is uncontrollable if and only if the length is…

This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain, we prove the null controllability of…

This article is dedicated to improve the controllability results obtained by Cerpa et al. in Commun. Contemp. Math 13 (2011) and by Micu et al. in Commun. Contemp. Math 11 (5) (2009) for a nonlinear coupled system of two Korteweg-de Vries…

This article gives a necessary first step to understanding the critical set phenomenon for the Korteweg-de Vries (KdV) equation posed on interval $[0,L]$ considering the Neumann boundary conditions with only one control input. We showed…

This paper deals with the null-controllability of a system of {\em mixed parabolic-elliptic pdes} at any given time $T>0$. More precisely, we consider the \textit{Kuramoto-Sivashinsky--Korteweg-de Vries equation} coupled with a second order…

This paper represents a new perspective in understanding the controllability of the Korteweg-de Vries (KdV) equation on unbounded domains. By studying the equation on both the right and left half-line with a single control input, we show…

We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control.The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates.Here, we go a step…

This paper studies the internal control of the Korteweg-de Vries-Burgers (KdVB) equation on a bounded domain. The diffusion coefficient is time-dependent and the boundary conditions are mixed in the sense that homogeneous Dirichlet and…

This paper is devoted to the local null controllability of the Burgers control system $y_t - y_{xx} + y y_x = u(t)$ on a bounded interval imposed by the zero Dirichlet boundary condition. It is known from the work of Marbach that this…

In this paper we study boundary controllability of the Korteweg-de Vries (KdV) equation posed on a finite domain $(0,L)$ with the Neumann boundary conditions: u_t+u_x+uu_x+u_{xxx}=0 in (0,L)x(0,T), u_{xx}(0,t)=0, u_x(L,t)=h(t),…

This paper is devoted to study boundary controllability of the Korteweg-de Vries equation posed on a finite interval, in which, because of the third-order character of the equation, three boundary conditions are required to secure the…

The aim of this work is to consider the controllability problem of the linear system associated to Korteweg-de Vries Burgers equation posed in the whole real line. We obtain a sort of exact controllability for solutions in $L^2_{loc}(\R^2)$…

In this article, we study the local exact controllability to a constant trajectory for a compressible Navier-Stokes-Korteweg system on the torus in dimension $ d\in\{1,2,3\}$ when the control acts on an open subset. To be more precise, we…

We consider the approximate control of solitons in generalized Korteweg-de Vries equations. By introducing a suitable internal bilinear control on the equation, we prove that any soliton is locally null controllable, and moreover, any…

We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…

We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in presence of quasi-linear perturbations, namely nonlinearities containing up to three…

We consider the nonlinear Korteweg-de Vries (KdV) equation in a bounded interval equipped with the Dirichlet boundary condition and the Neumann boundary condition on the right. It is known that there is a set of critical lengths for which…

In this paper, we investigate the quantitative exponential stability of the Korteweg-de Vries equation on a finite interval with its length close to the critical set. Sharp decay estimates are obtained via a constructive PDE control…