Nonlinear degenerate parabolic equations with time-dependent singular potentials for Baouendi-Grushin vector fields

In this paper, we are concerned with the following three types of nonlinear degenerate parabolic equations with time-dependent singular potentials: .uq.t=...(.z..p.|..u|p.2..u)+V(z,t)up.1,.uq.t=...(.z..2...u m)+V(z,t)um,.uq.t=u....(u.|..u|p.2..u)+V(z,t)up.1+.+. in a cylinder . . (0, T) with initial condition u (z, 0) = u 0 (z) . 0 and vanishing on the boundary .. . (0, T), where . is a Carnot-Carathéodory metric ball in .d+k and the time-dependent singular potential function is V (z, t) . L 1loc (. . (0, T)). We investigate the nonexistence of positive solutions of these three problems and present our results on nonexistence.