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We study positive blowing-up solutions of systems of the form: $$u_t=\delta_1\Delta u+e^{pv},\quad v_t= \delta_2\Delta v+e^{qu},$$ with$\delta_1,\delta_2>0$ and $p, q>0$. We prove single-point blow-up for largeclasses of radially decreasing solutions. This answers a question left open ina paper of Friedman and Giga~(1987), where the result was obtained only for theequidiffusive case $\delta_1=\delta_2$ and the proof depended crucially on thisassumption.

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