Fredholm Transform and Local Rapid Stabilization for a Kuramoto-Sivashinsky Equation

2015/01/09 by Jean‐Michel Coron, Qi Lü, Coron, Jean-Michel +1 · 4 citations
Engineering · Computer Science · #Stability and Controllability of Differential Equations #Nonlinear Dynamics and Pattern Formation #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1501.02042

Abstract

This paper is devoted to the study of the local rapid exponential stabilization problem for a controlled Kuramoto-Sivashinsky equation on a bounded interval. We build a feedback control law to force the solution of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates, provided that the initial datum is small enough. Our approach uses a method we introduced for the rapid stabilization of a Korteweg-de Vries equation. It relies on the construction of a suitable integral transform and can be applied to many other equations.

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• Rapid stabilization of the heat equation with localized disturbance
• Rapid stabilization for a wave equation with boundary disturbance
• F-equivalence for parabolic systems and applications to the stabilization of nonlinear PDE
• On the controllability of the Kuramoto-Sivashinsky equation on multi-dimensional cylindrical domains

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