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

Encyclopedia of Systems and Control

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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 waves 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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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Avda. España 1680, Valparaiso, Chile

    Eduardo Cerpa

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  1. Eduardo Cerpa
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Correspondence to Eduardo Cerpa .

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Editors and Affiliations

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

    John Baillieul

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

    Tariq Samad

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Cerpa, E. (2013). 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_13-1

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

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  • Online ISBN: 978-1-4471-5102-9

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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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