Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities

We study positive blowing-up solutions of systems of the form: ut=δ1Δu+epv,vt=δ2Δv+equ, with δ1,δ2>0δ1,δ2>0 and p,q>0p,q>0. We prove single-point blow-up for large classes of radially decreasing solutions. This answers a question left open in a paper of Friedman and Giga (1987), where the result was obtained only for the equidiffusive case δ1=δ2δ1=δ2 and the proof depended crucially on this assumption.