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

Glass Olivier | Zendy; Guerrero Sergio | Zendy

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

Author(s) -

Glass Olivier,

Guerrero Sergio

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200701006

Subject(s) - controllability , korteweg–de vries equation , mathematics , dirichlet boundary condition , limit (mathematics) , zero (linguistics) , nonlinear system , mathematical analysis , bounded function , boundary (topology)

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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