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.
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