“…Throughout this paper we suppose that a(x, t), b(x, t), k(x, y, t) and u 0 (x) satisfy the following conditions: a(x, t), b(x, t) ∈ C α loc (Ω × [0, ∞)), 0 < α < 1, a(x, t) ≥ 0, b(x, t) ≥ 0; k(x, y, t) ∈ C(∂Ω × Ω × [0, ∞)), k(x, y, t) ≥ 0; u 0 (x) ∈ C(Ω), u 0 (x) ≥ 0, x ∈ Ω, u 0 (x) = Ω k(x, y, 0)u l 0 (y) dy, x ∈ ∂Ω. For global existence and blow-up of solutions for parabolic equations with nonlocal boundary conditions we refer to [1,2,6], [11]- [18], [21,23,24,30,32,33] and the references therein. Initial-boundary value problems for nonlocal parabolic equations with nonlocal boundary conditions were considered in many papers also (see, for example, [4,7,9,10,26,27,34]).…”