Exact controllability of non-Lipschitz semilinear systems

Abstract

We present sufficient conditions for exact controllability of a semilinear infinite dimensional dynamical system. The system mild solution is formed by a noncompact semigroup and a nonlinear disturbance that does not need to be Lipschitz continuous. Our main result is based on a fixed point type application of the Schmidt existence theorem and illustrated by a nonlinear transport partial differential equation.