THE SEMI-CLASSICAL SOLUTION FOR A CLASS OF SEMILINEAR INITIAL VALUE CONTROL PROBLEMS IN BANACH SPACE

In this paper, the local existence and uniqueness of S-classical solution of a class of semilinear initial value control problems which defined as: d/dt [ zw (t)+g(t، zw (t)) ] =Azw (t) f(t، zw (t)) +Bw (t)، t › 0zw(0)=z0 have been discussed and proved in suitable Banach spaces. All results are obtained by using Banach contraction principle and depending on the theory of analytic semigroup of control problems.