Thumbnail

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

View/Open
Type
Article accepté pour publication ou publié
Date
2008
Journal name
Asymptotic Analysis
Volume
60
Number
1-2
Publisher
IOS Press
Pages
61-100
Publication identifier
Metadata
Show full item record
Author(s)
Glass, Olivier
Guerrero, Sergio
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 / Keywords
Controllability; KdV equation; zero dispersion limit