INSENSITIZING CONTROL PROBLEM FOR THE KAWAHARA EQUATION
Résumé
This paper deals with the existence of insensitizing control for a nonlinear dispersive equation, namely Kawahara equation. Roughly speaking, the underlying problem is to find a distributed control such that $L^2$-norm of the state in some subregion is insensitive with respect to small perturbations in the initial data.
The problem of finding an insensitizing control is first reduced to a null controllability problem for an extended cascade system using some standard arguments. Next, to solve this null controllability problem we first establish null controllability of the associated linearized system using suitable Carleman estimates for the corresponding adjoint system, and then use the well known inverse mapping theorem to conclude the desired controllability result for the main nonlinear extended cascade system.
Mots clés
Mathematics Subject Classification. 35K52 -35Q53 -93B05 -93B07 -93B35 Kawahara equation insensitizing control Carleman estimate observability inverse mapping theorem
Mathematics Subject Classification. 35K52 -35Q53 -93B05 -93B07 -93B35 Kawahara equation
insensitizing control
Carleman estimate
observability
inverse mapping theorem
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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