Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit
Glass, Olivier; Guerrero, Sergio (2008), Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit, Asymptotic Analysis, 60, 1-2, p. 61-100. http://dx.doi.org/10.3233/ASY-2008-0900
TypeArticle accepté pour publication ou publié
Journal nameAsymptotic Analysis
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Abstract (EN)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.
Subjects / KeywordsControllability; KdV equation; zero dispersion limit
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