On the solvability of parabolic functional differential equations in banach spaces

In this paper, a parabolic functional differential equation is considered in the spaces C(0; T;H1 p (Q)) for p close to 2. The transformations of the space argument are supposed to be multiplicators of the Sobolev spaces with a small smoothness exponent. The machinery of the investigation is based on the semigroup theory. In particular, it is proved that the elliptic part of the operator is a generator of a strongly continuous semigroup. © The Eurasian National University