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Null Controllability with Constraints on the State for the Korteweg-de Vries Equation

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Abstract

This paper is concerned with a null controllability problem for the Korteweg-de Vries equation with finite number of constraints on the state. We first let the equation evolve freely on a small time interval. Then, we consider the linearized system on the rest interval. Transforming the linearized problem into an equivalent problem of null controllability with constraints on the control, we solve the equivalent problem using an adapted Carleman estimate. Finally, by a fixed-point argument, we obtain the main result.

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Acknowledgement

I sincerely thank Professor Yong Li for many useful suggestions and help.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, P.R. China

    Mo Chen

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  1. Mo Chen
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Correspondence to Mo Chen.

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Chen, M. Null Controllability with Constraints on the State for the Korteweg-de Vries Equation. Acta Appl Math 146, 17–28 (2016). https://doi.org/10.1007/s10440-016-0055-4

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  • DOI: https://doi.org/10.1007/s10440-016-0055-4

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