Existence and nonexistence results for a class of parabolic equations with mixed boundary conditions

Abstract

We study the following parabolic problem {ut - div(|x| -pγ|∇u|p-2∇u) = λf(x, u), u ≥ 0 in Ω × (0, T), B(u) = 0 on ∂Ω × (0, T), (0.1) u(x, 0) = φ(x) if x ∈ Ω, where Ω ⊂ IRN is a smooth bounded domain with 0 ∈ Ω, B(u) ≡ uΧ ∑1×(0, T) + |x|-pγ|∇u| p-2∂u/∂vΧ∑2×(0, T) and -∞ < γ 0.