Abstract:
In the paper we consider the generalized solvability of boundary value problem for the loaded
parabolic
equations with irregular coefficients. Theorem on unique solvability of the boundary value problem
is proved. The correctness of the theorem and the accuracy of selected functional spaces are
established by obtained a priori estimates. The proof of the theorem is carried out using the
theory of Sobolev spaces, the method of a priori estimates, and the Galerkin method. Along with the
initial boundary value problem, the corresponding adjoint boundary value problem is investigated.
To prove the solvability of the adjoint
problem, we define a linear continuous form and use the duality relations.
