Blow-up estimates of positive solutions of a parabolic system (Q1336314)

The paper deals with estimates from above near the blow-up point for a class of positive solutions of the system \[ u_ t = \Delta u + v^ p, \quad v_ t = \Delta v + u^ q \] in a cylinder whose bottom is a ball in \(\mathbb{R}^ n\) centered at the origin and \(p\), \(q>1\). The system is subjected to homogeneous Dirichlet boundary conditions. The result of the paper is an extension to the above system of the results of Fred B. Weissler which concerns the equation \(u_ t = \Delta u + u^ p\).