Abstract
In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: \begin{center} \(\begin{cases} \Delta_p u= v^m| \nabla u |^\alpha& \text{in}\quad \Omega\\ \Delta_p v= v^\beta| \nabla u |^q & \text{in}\quad \Omega, \end{cases}\) \end{center} where \(\Omega\subset\mathbb{R}^N(N\geq 2)\) 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 \(\R^3\).