Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit

Article type: Research Article

Authors: Glass, O. | Guerrero, S.

Affiliations: Université Pierre et Marie Curie-Paris 6, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, F-75005 France. E-mails: {glass, guerrero}@ann.jussieu.fr

Abstract: In this paper, we deal with controllability properties of linear and nonlinear Korteweg–de Vries equations in a bounded interval. The main part of this paper is a result of uniform controllability of a linear KdV equation in the limit of zero-dispersion. Moreover, we establish a result of null controllability for the linear equation via the left Dirichlet boundary condition, and of exact controllability via both Dirichlet boundary conditions. As a consequence, we obtain some local exact controllability results for the nonlinear KdV equation.

Keywords: controllability, KdV equation, zero dispersion limit

DOI: 10.3233/ASY-2008-0900

Journal: Asymptotic Analysis, vol. 60, no. 1-2, pp. 61-100, 2008