劈形算符
爆炸
欧米茄
数学
球(数学)
半径
边界(拓扑)
组合数学
数学分析
数学物理
物理
量子力学
计算机安全
计算机科学
作者
Ahmed Bachir,Jacques Giacomoni,Guillaume Warnault
出处
期刊:Differential and Integral Equations
日期:2022-09-01
卷期号:35 (9/10)
标识
DOI:10.57262/die035-0910-511
摘要
In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: $$ \begin{cases} \Delta_p u= v^m| \nabla u |^\alpha & \text{in}\quad \Omega\\ \Delta_p v= v^\beta| \nabla u |^q & \text{in}\quad \Omega, \end{cases} $$ where $\Omega\subset\mathbb{R}^N\ (N\geq 1)$ is either equal to $ \mathbb{R}^N $ or equal to a ball $B_R$ centered at the origin and having radius $R>0$, $1 < p < \infty$, $m,q > 0$, $\alpha\geq 0$, $0\leq \beta\leq m$ and $\delta:=(p-1-\alpha)(p-1-\beta)-qm \neq 0$. 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 $\mathbb{R}^3$.
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