Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Boundary Control of Korteweg-de Vries and Kuramoto-Sivashinsky PDEs

  • Eduardo CerpaEmail author
Living reference work entry

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DOI: https://doi.org/10.1007/978-1-4471-5102-9_13-2

Abstract

The Korteweg-de Vries (KdV) and the Kuramoto-Sivashinsky (KS) partial differential equations are used to model nonlinear propagation of one-dimensional phenomena. The KdV equation is used in fluid mechanics to describe wave propagation in shallow water surfaces, while the KS equation models front propagation in reaction-diffusion systems. In this article, the boundary control of these equations is considered when they are posed on a bounded interval. Different choices of controls are studied for each equation.

Keywords

Controllability Stabilizability Higher-order partial differential equations Dispersive equations Parabolic equations 
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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile

Section editors and affiliations

  • Miroslav Krstic
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaSan Diego, La JollaUSA