On boundary value problems for essentially loaded parabolic equations in bounded domains

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 L ₂( 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 L ₂(0 , 1) and L ₂( 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.