Nonlinear degenerate parabolic equations with singular coefficients for Greiner vector fields

In this work, we consider the following nonlinear parabolic partial differential equations: (Formula presented.) in a cylinder Ω × (0, T) with initial condition u(w, 0) = u ₀ (w) ≥ 0 and vanishing on the boundary ∂Ω × (0, T), where Ω is a Carnot Carathéodory metric ball in ℝ ²ⁿ⁺¹ with smooth boundary and the time-dependent potential function is (Formula presented.), 0 < m < q and 1 < p < q + 1. We investigate the nonexistence of positive solutions of these two problems and present our results on nonexistence.