On the non-uniform null controllability of a linear KdV equation

Article type: Research Article

Authors: Carreño, N.^{a; *} | Guerrero, S.^b

Affiliations: [a] Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile. E-mail: nicolas.carrenog@usm.cl | [b] Laboratoire Jacques-Louis Lions, UMR 7598, Université Pierre et Marie Curie, Paris, France. E-mail: guerrero@ann.jussieu.fr

Correspondence: [*] Corresponding author: N. Carreño, Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile. E-mail: nicolas.carrenog@usm.cl.

Abstract: In this paper we consider a linear KdV equation with a transport term posed on a finite interval with the boundary conditions considered by Colin and Ghidaglia. The main results concern the behavior of the cost of null controllability with respect to the dispersion coefficient when the control acts on the left endpoint. In particular, for any final time we prove that this cost grows exponentially as the dispersion coefficient vanishes and the transport coefficient is negative.

Keywords: uniform controllability, dispersion limit, Carleman inequalities

DOI: 10.3233/ASY-151300

Journal: Asymptotic Analysis, vol. 94, no. 1-2, pp. 33-69, 2015