Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities. (June 2016)

• Record Type: Journal Article
• Authors: Souplet, Philippe; Tayachi, Slim
• Is Part Of: Nonlinear analysis. Volume 138(2016)
• Page Start: 428
• Page End: 447
• Publication Date: 2016-06
• Subjects: primary 35B40 35B45 35B50 -- secondary 35K60 35K57; Reaction–diffusion systems -- Exponential nonlinearities -- Single-point blow-up; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.01.008
• Languages: English
• ISSNs: 0362-546X

Abstract

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.