The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms
Volume 102 / 2011
Annales Polonici Mathematici 102 (2011), 187-203
MSC: 35K15, 35K65.
DOI: 10.4064/ap102-2-6
Abstract
This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources $u^p(x_0,t)$, $v^n(x_0,t)$, local sources $u^m(x,t)$, $v^q(x,t)$, and weight functions $a(x), b(x)$, on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases $m, q \leq 1$ or $m, q>1$, but also for $m>1 \mathbin {\&}q<1$ or $m<1\mathbin {\&}q>1$.
