On some nonlocal parabolic boundary value problems

We study the question of solvability of the nonlocal boundary value problems for operator-differential equations of the first order with operators, which are generators of analytical semigroups. We establish existence and uniqueness of theorems for these boundary value problems under certain conditions on the data of the problem. The Sobolev-Besov spaces are employed. The results obtained are applied to the study of nonlocal boundary value problems for parabolic equations and systems.