# American Institute of Mathematical Sciences

January  2018, 38(1): 209-230. doi: 10.3934/dcds.2018010

## Single-point blow-up for a multi-component reaction-diffusion system

 Université de Tunis El Manar, Faculté des Sciences de Tunis, Département de Mathématiques, Laboratoire Équations aux Dérivées Partielles LR03ES04, Tunis, 2092, Tunisie

Received  December 2016 Revised  July 2017 Published  September 2017

In this work, we prove single-point blow-up for any positive, radially decreasing, classical and blowing-up solution of a system of $m≥q3$ heat equations in a ball of $\mathbb{R}^n$, which are coupled cyclically by superlinear monomial reaction terms. We also obtain lower pointwise estimates for the blow-up profiles.

Citation: Nejib Mahmoudi. Single-point blow-up for a multi-component reaction-diffusion system. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 209-230. doi: 10.3934/dcds.2018010
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