On refined blowup estimates for the exponential reaction-diffusion equation

TL;DR

This paper provides simplified proofs of sharp upper estimates for blowup profiles and refined space-time behavior of radial solutions to the exponential reaction-diffusion equation, unifying various estimates into a global framework.

Contribution

It introduces a new, simplified method to derive sharp upper bounds for blowup profiles and space-time behavior in exponential reaction-diffusion equations.

Findings

Established a global upper space-time estimate for solutions.

Derived sharp upper bounds for the final blowup profile.

Unified various estimates into a comprehensive framework.

Abstract

We consider radial decreasing solutions of the semilinear heat equation with exponential nonlinearity. We provide a relatively simple proof of the sharp upper estimates for the final blowup profile and for the refined space-time behavior. We actually establish a global, upper space-time estimate, which contains those of the final and refined profiles as special cases.