Null Controllability and Stabilization of the Linear Kuramoto-sivashinsky Equation
نویسندگان
چکیده
In this article, we study the boundary controllability of the linear Kuramoto-Sivashinsky equation on a bounded interval. The control acts on the first spatial derivative at the left endpoint. First, we prove that this control system is null controllable. It is done using a spectral analysis and the method of moments. Then, we introduce a boundary feedback law stabilizing to zero the solution of the closed-loop system.
منابع مشابه
Boundary local null-controllability of the Kuramoto-Sivashinsky equation
We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the nullcontrollability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equatio...
متن کاملNull Controllability of the Stabilized Kuramoto-Sivashinsky System with One Distributed Control
This paper presents a control problem for a one-dimensional nonlinear parabolic system, which consists of a Kuramoto–Sivashinsky–Korteweg de Vries equation coupled to a heat equation. We address the problem of controllability by means of a control supported in an interior open subset of the domain and acting on one equation only. The local null-controllability of the system is proved. The proof...
متن کاملExact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
متن کاملFeedback control of the Kuramoto – Sivashinsky equation
This work focuses on linear finite-dimensional output feedback control of the Kuramoto–Sivashinsky equation (KSE) with periodic boundary conditions. Under the assumption that the linearization of the KSE around the zero solution is controllable and observable, linear finite-dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution, for any value of ...
متن کاملA Fully Nonlinear Equation for the Flame Front in a Quasi-steady Combustion Model
We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasisteady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null ...
متن کامل