Initial and boundary blow-up problem for p-Laplacian parabolic equation with general absorption

2014/06/04 by Mingxin Wang, Wang, Mingxin, Peter Y. H. Pang +3
Computer Science · Mathematics · #35B30 #35J25 #35K20 #35K60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1406.0989

openalex publication_date 2014/06/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this article, we investigate the initial and boundary blow-up problem for the p-Laplacian parabolic equation u_t-Δ_p u=-b(x,t)f(u) over a smooth bounded domain Ω of ℝ^N with N≥2, where Δ_pu=\rm div(|∇ u|^p-2∇ u) with p>1, and f(u) is a function of regular variation at infinity. We study the existence and uniqueness of positive solutions, and their asymptotic behaviors near the parabolic boundary.

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