On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains

2008/07/20 by Waad Al Sayed, Sayed, Waad Al, Laurent Veron +1
Mathematics · #34 #35K60 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34 #msc:35K60

paper · pdf · doi:10.48550/arxiv.0807.3177

16 pages

arxiv created 2008/08/14 · arxiv updated 2009/12/01

Abstract

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

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