A simple proof of the approximate controllability from the interior for nonlinear evolution problems

Abstract

The approximate controllability property for solutions of a large class of nonlinear evolution problems is obtained under some abstract conditions which hold, for instance, when the control is the right hand side of the equation. Our very simple method put in evidence the independence between the solvability of a boundary value problems and the study of the approximate controllability property which takes places in a number of cases. No duality type arguments are used which allows the consideration of very general nonlinear problems.