... are very natural for solvability of parabolic initial-boundary value problems These spaces as well as the solvability have been investigated by Slobodecki˘ [9], Agranoviˇ and Viˇik [1], V ı c ... Solonnikov, and N N Uralzeva, Linear and Quasi-Linear Equations of Parabolic Type, American Mathematical Society, Rhode Island, 1968 [6] J.-L Lions and E Magenes, Non-Homogeneous Boundary Value Problems ... (x,t) ∈ Ω+ × R+ (3.6) 10 On explicit and numerical solvability Let us note that since the functions fk,r are linearly independent and the operator in the right-hand side of (3.6) is invertible, then...