JournalsaihpcVol. 26, No. 2pp. 457–475

Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain

  • Eduardo Cerpa

    Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, Bât. 425, 91405 Orsay Cedex, France

  • Emmanuelle Crépeau

    INRIA Rocquencourt, Domaine de Voluceau, 78150 Le Chesnay, France, Université de Versailles Saint-Quentin en Yvelines, 78035 Versailles, France
Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain cover
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Abstract

It is known that the linear Korteweg–de Vries (KdV) equation with homogeneous Dirichlet boundary conditions and Neumann boundary control is not controllable for some critical spatial domains. In this paper, we prove in these critical cases, that the nonlinear KdV equation is locally controllable around the origin provided that the time of control is large enough. It is done by performing a power series expansion of the solution and studying the cascade system resulting of this expansion.

Cite this article

Eduardo Cerpa, Emmanuelle Crépeau, Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 2, pp. 457–475

DOI 10.1016/J.ANIHPC.2007.11.003