Internal controllability of the Korteweg-de Vries equation on a bounded domain

By R. C. Filho, Ademir Fernando Pazoto, Lionel Rosier. 2014

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This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain, we prove the null controllability of the KdV equation by means of a new Carleman inequality. As a consequence, we obtain a regional controllability result, the state function being controlled on the left part of the complement of the control region. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted L2 space is also established.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/7712aafab096a5d9e7895c95fac61d1102c71143