In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials:
$$\begin{array}{*{20}c}
{\frac{{\partial u^q }}
{{\partial t}} = \nabla _\alpha \cdot \left( {\left\| z \right\|^{ - p\gamma } \left| {\nabla _\alpha u} \right|^{p - 2} \nabla _\alpha u} \right) + V(z,t)u^{p - 1} ,} \\
{\frac{{\partial u^q }}
{{\partial t}} = \nabla _\alpha \cdot \left( {\left\| z \right\|^{ - 2\gamma } \nabla _\alpha u^m } \right) + V(z,t)u^m ,} \\
{\frac{{\partial u^q }}
{{\partial t}} = u^\mu \nabla _\alpha \cdot \left( {u^\tau \left| {\nabla _\alpha u} \right|^{p - 2} \nabla _\alpha u} \right) + V(z,t)u^{p - 1 + \mu + \tau } } \\
\end{array}$$
in a cylinder Ω × (0, *T*) with initial condition *u* (*z*, 0) = *u*_{0} (*z*) ≥ 0 and vanishing on the boundary *∂*Ω × (0, T), where Ω is a Carnot-Carathéodory metric ball in ℝ^{d+k} and the time-dependent singular potential function is *V* (*z, t*) ∈ *L*_{loc}^{1}
(Ω × (0, *T*)). We investigate the nonexistence of positive solutions of these three problems and present our results on nonexistence.