In this paper, we consider the Dirichlet and Neumann problems in the domain $П^+_{(0;T]}:=\{(t,x)∈(0,T], x ∈ \mathbb{R}^n_+\}, \mathbb{R}^n_+ :=\{x := (x_1,...,x_n) ∈ \mathbb{R}^n|x_n > 0\}$ , for two second-order parabolic equations. In both equations, the coefficients at the second-order derivatives with respect to $x$ are constant, and the coefficients at the first-order derivatives with respect to $x_j$ are functions $bx_j+a_j, j ∈ \{1,...,n\}$ where $\{b,a_j\}⊂\mathbb{R}^1$, moreover $b≠0$ and $a_n=0$. The second equation also contains degeneration at $t = 0$. For such problems, Green’s vector functions are constructed, estimates of the components of these functions and their derivatives are obtained. In order to construct the Green’s vector functions we use the fundamental solutions of the Cauchy problem for the equations and parabolic potentials of the simple and double layers. The obtained results could be used for establishing the correct solvability of the boundary value problems, integral representation and the properties of their solutions.

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