Distributed control problems for a class of degenerate semilinear evolution equations

The unique solvability in the sense of strong solution of initial problems for a class of semilinear first order differential equations in Banach spaces with degenerate operator at the derivative is studied. It allows to prove the existence of a solution for the optimal control problem to systems, described by these initial problems. Abstract results are illustrated by the examples of degenerate systems of partial differential equations not solvable with respect to the time derivatives and of optimal control problems for them.