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

We study positive blowing-up solutions of systems of the form: $u_t=δ_1 Δu+e^{pv},\quad v_t= δ_2Δv+e^{qu},$ with $δ_1,δ_2>0$ and $p, q>0$. 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 $δ_1=δ_2$ and the proof depended crucially on this assumption.

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