Abstract:
In the paper we study issues of a strong solution for "essentially" loaded differential equations of the
parabolic type in bounded domains. Features of the problems under consideration: for example, in the
L2(Q) space the corresponding differential operators are not closure operators, since firstly, the load does
not obey the corresponding differential part of the considered operator, that is, for its differential part the
load is not a weak perturbation. Secondly, it is obvious that load operators in the spaces L2(0; 1) and L2(Q)
are not closure operators. This indicates that it is impossible to directly investigate the issues of the strong
solution to boundary value problems for non-closed loaded differential equations. However, the study of
equations [1-4] give theoretical character, but also a clear applied [5-7] character.
