Blow-up profiles of solutions for the exponential reaction-diffusion equation

TL;DR

This paper investigates the final blow-up profiles of solutions to a reaction-diffusion equation with exponential reaction terms, using semigroup estimates, and extends the approach to power nonlinearities.

Contribution

It identifies the final blow-up profile for solutions with exponential reaction terms and demonstrates that the same method applies to power nonlinearities.

Findings

Final blow-up profile characterized for exponential reaction-diffusion solutions.

Method applicable to both exponential and power nonlinearities.

Provides a unified approach using semigroup estimates.

Abstract

We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up profile. Our aim is to find the final time blow-up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach works also for the power nonlinearity.