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

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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)