The $L_2$-theory of generalized solutions of general linear model parabolic boundary value problems

General linear model parabolic boundary value problems are studied (in a revised formulation) in the Sobolev spaces $\mathscr H^s(\Omega)$ ($-\infty<s<\infty$) of generalized functions (distributions) –the $L_2$-theory. The well-posed solvability of these problems in suitable function spaces is proved.
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