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

Abstract

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