Boundary blow-up rates of large solutions for quasilinear elliptic equations with convention terms (Q2857751)

The authors of this paper study the following problem NEWLINE\[NEWLINE-\Delta_p u\pm|\nabla u|^{q(p-1)}=b(x)f(u)\text{ in }\Omega ,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu=+\infty\text{ on }\partial\Omega ,NEWLINE\]NEWLINE where \(\Omega\) is a smooth bounded domain of \(\mathbb R^N\), \(N>2\), with smooth boundary \(\partial \Omega\), \(1<p<+\infty\), \(b\in C(\Omega)\) is a non-negative function in \(\Omega\) and the nonlinear term \(f\in C^2([0, +\infty))\) is increasing in \([0, +\infty)\) and such that \(f(0)=0\). NEWLINENEWLINENEWLINEUnder suitable conditions on the exponent \(q\) and additional assumptions on \(b\) and \(f\), the authors study the asymptotic behavior of the large solution of the problem near the boundary \(\partial \Omega\).