This paper deals with the existence of insensitizing control for a nonlinear dispersive equation, namely the Kawahara equation. Roughly speaking, the underlying problem is to find a distributed control such that the \(L^2\) -norm of the state in some subregion is insensitive 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.
