Partial asymptotic null controllability for semilinear evolution equations in Hilbert spaces

Abstract

This work deals with the problem of partial asymptotic null controllability for constrained systems governed by semi-linear evolution equations, where the linear part generates a strongly continuous compact semigroup on Hilbert spaces. This consists of driven only a desired part of the system's state to the origin, taking into account mixed state-input constraints. We give sufficient conditions for the existence of appropriate control laws to ensure partial asymptotic null controllability. The explicit expression of such controls is given as strongly-weakly continuous selections of a set-valued map which is defined through a certain practical tangential condition. Application to semilinear parabolic partial differential equations is treated in order to illustrate the results established.