Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. (June 2016) - Souplet, Philippe; Tayachi, Slim
Abstract: We study positive blowing-up solutions of systems of the form: u t = δ 1 Δ u + e p v, v t = δ 2 Δ v + e q u, 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.