Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit |
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| Authors: | Olivier Glass Sergio Guerrero |
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| Affiliation: | Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boite courrier 187, 75252 Paris Cedex 05, France |
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| 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. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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