Nonlinear degenerate parabolic equations with singular coefficients for Greiner vector fields

Abstract

In this work, we consider the following nonlinear parabolic partial differential equations: 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 Caratheodory metric ball in ℝ2n+1 with smooth boundary and the time-dependent potential function is , 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.