On the Exponential Stability of a Nonlinear Kuramoto–Sivashinsky–Korteweg-de Vries Equation with Finite Memory

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Boumediène Chentouf
Keyword(s):  
Exponential Stability ◽  
Vries Equation ◽  
De Vries ◽  
Finite Memory

scholarly journals Control and stabilization of the periodic fifth order Korteweg-de Vries equation

2019 ◽  
Vol 25 ◽  
pp. 38
Author(s):  
Cynthia Flores ◽  
Derek L. Smith
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Vries Equation ◽  
Regularity Property ◽  
Contraction Principle ◽  
Smoothing Effect ◽  
Dissipative Term ◽  
De Vries ◽  
Fifth Order

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in Hs(𝕋), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regularity property, yields a smoothing effect permitting the application of the contraction principle.

scholarly journals On the semi-global stabilizability of the Korteweg-de Vries Equation via model predictive control

2018 ◽  
Vol 24 (1) ◽  
pp. 237-263 ◽  
Author(s):  
Behzad Azmi ◽  
Anne-Céline Boulanger ◽  
Karl Kunisch
Keyword(s):  
Model Predictive Control ◽  
Numerical Experiment ◽  
Exponential Stability ◽  
Predictive Control ◽  
Vries Equation ◽  
Kdv Equation ◽  
Bounded Interval ◽  
De Vries ◽  
The Stability ◽  
Theoretical Results

Stabilization of the nonlinear Korteweg-de Vries (KdV) equation on a bounded interval by model predictive control (MPC) is investigated. This MPC strategy does not need any terminal cost or terminal constraint to guarantee the stability. The semi-global stabilizability is the key condition. Based on this condition, the suboptimality and exponential stability of the model predictive control are investigated. Finally, numerical experiment is presented which validates the theoretical results.

scholarly journals On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Julie Valein
Keyword(s):  
Asymptotic Stability ◽  
Exponential Stability ◽  
Numerical Simulations ◽  
Vries Equation ◽  
Stability Result ◽  
Internal Feedback ◽  
De Vries

<p style='text-indent:20px;'>The aim of this work is to study the asymptotic stability of the nonlinear Korteweg-de Vries equation in the presence of a delayed term in the internal feedback. We first consider the case where the weight of the term with delay is smaller than the weight of the term without delay and we prove a semiglobal stability result for any lengths. Secondly we study the case where the support of the term without delay is not included in the support of the term with delay. In that case, we give a local exponential stability result if the weight of the delayed term is small enough. We illustrate these results by some numerical simulations.</p>

scholarly journals Exponential stabilization of a linear Korteweg-de Vries equation with input saturation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ahmat Mahamat Taboye ◽  
Mohamed Laabissi
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Vries Equation ◽  
Input Saturation ◽  
Loop System ◽  
Exponential Stabilization ◽  
Closed Loop System ◽  
De Vries ◽  
Exponentially Stable ◽  
Well Posed

<p style='text-indent:20px;'>This article deals with the issue of the exponential stability of a linear Korteweg-de Vries equation with input saturation. It is proved that the system is well-posed and the origin is exponentially stable for the closed loop system, by using the classical argument used in this kind of problems.</p>

Integration of the nonlinear modified Korteweg-de Vries equation with a loaded term

2020 ◽  
Vol 2020 (2) ◽  
pp. 85-98
Author(s):  
A.B. Khasanov ◽  
T.J. Allanazarova
Keyword(s):  
Vries Equation ◽  
De Vries ◽  
Loaded Term

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

scholarly journals A flux reconstruction method for the Korteweg-de Vries equation

2021 ◽  
Vol 1978 (1) ◽  
pp. 012031
Author(s):  
Ningbo Guo ◽  
Yaming Chen ◽  
Xiaogang Deng
Keyword(s):  
Vries Equation ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
De Vries
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