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Encyclopedia of Systems and Control pp 1–6Cite as

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

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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.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile

    Eduardo Cerpa

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  1. Eduardo Cerpa
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Correspondence to Eduardo Cerpa .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA

    Miroslav Krstic

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Cerpa, E. (2020). Boundary Control of Korteweg-de Vries and Kuramoto-Sivashinsky PDEs. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_13-2

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

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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Chapter history

  1. Latest

    Boundary Control of Korteweg-de Vries and Kuramoto-Sivashinsky PDEs
    Published:
    07 November 2019

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

  2. Original

    Boundary Control of Korteweg-de Vries and Kuramoto-Sivashinsky PDEs
    Published:
    15 March 2014

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

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