Revisit on the blow-up rate of solutions for a weakly coupled system of semilinear heat equations in the subcritical case

TL;DR

This paper presents a simple method to analyze finite-time blow-up of solutions in weakly coupled semilinear heat equations, providing lifespan estimates and blow-up rate bounds in the subcritical case.

Contribution

It introduces a straightforward approach to study blow-up phenomena and derives lifespan and blow-up rate estimates for coupled heat equations.

Findings

Solutions blow up in finite time under subcritical conditions

Lifespan estimates for solutions are provided

Lower bounds for blow-up rates are established

Abstract

We introduce a straightforward method to analyze the blow-up of systems of ordinary differential inequalities, and apply it to study the blow- up of solutions to a weakly coupled system of semilinear heat equations. We prove that the solution blows up in a finite time under the subcritical condition. Moreover, we give estimates of lifespan of the solution and lower estimates of the blow-up rate for a localized average of each component.