Asymptotic behavior of blowing-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids

2021/12/28 by Ahmed Bachir, Jacques Giacomoni, Bachir, Ahmed +3
Computer Science · Mathematics · #35B40 #35J47 #35J92 #70G60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.14277

openalex publication_date 2021/12/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: \begincases Δ_p u= v^m| ∇ u |^α& in Ω Δ_p v= v^β| ∇ u |^q & in Ω, \endcases where Ω⊂ℝ^N(N≥ 2) is either equal to ℝ^N or equal to a ball B_R centered at the origin and having radius R>0, 10, α≥ 0, 0≤ β≤ m and δ:=(p-1-α)(p-1-β)-qm ≠ 0. Our aim is to establish the asymptotics of the blowing-up radial solutions to the above system. Precisely, we provide the accurate asymptotic behavior at the boundary for such blowing-up radial solutions. For that,we prove a strong maximal principle for the problem of independent interest and study an auxiliary asymptotically autonomous system in \R³.

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