Controllability of Semilinear Systems of Parabolic Equations with Delay on the State

In this paper we prove the approximate controllability of the following semilinear system parabolic equations with delay on the state variable where Ω is a bounded domain in is a n × n non diagonal matrix whose eigenvalues are semi‐simple with non negative real part, the control u belongs to and B is a n × m matrix. Here τ≥0 is the maximum delay, which is supposed to be finite. We assume that the operator L:L²(?τ,0];Z)→Z is linear and bounded with and the nonlinear function f:0,r] × IRⁿ×IR^m→IRⁿ is smooth and bounded.