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

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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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Author information

Authors and Affiliations

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

    Eduardo Cerpa

Authors
  1. Eduardo Cerpa
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Editor information

Editors and Affiliations

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

    John Baillieul

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

    Tariq Samad

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Cerpa, E. (2015). 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/10.1007/978-1-4471-5058-9_13

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