Nonlinear degenerate parabolic equations with time dependent singular coefficients

We are concerned with the nonexistence of positive solutions of the nonlinear parabolic partial differential equations in a cylinder Ω × (0, T) with initial condition u(, 0) = u₀ ≥ 0 and vanishing on the boundary ∂Ω × (0, T), given by where Ω ∈ R_n (resp. a Carnot Carathéodory metric ball in with smooth boundary and the time dependent singular potential function V(x, t) ∈ L¹_loc(Ω × (0, T)), 1 < p < N, p - 1 + α + β > 0. We find the best lower bounds for p + β and provide proofs for the nonexistence of positive solutions.