On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains

Abstract

Abstract We study the existence and uniqueness of the positive solutions of the problem (P): Әtu - Δu + uq = 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L1(Ω), when Ω is a bounded domain in ℝN. We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N - 2) and it is unique if ӘΩ = ӘΩ̅c. If ӘΩ has the local graph property, we prove that there exists at most one solution to problem (P).