# Blowup versus global in time existence of solutions for nonlinear heat equations

## TL;DR

This paper presents a straightforward proof of solution blowup for nonlinear heat equations, using Morrey space norms, complementing existing conditions for global existence, and extending Fujita's method to other nonlinear parabolic equations.

## Contribution

It introduces a simple blowup criterion based on Morrey space norms and extends Fujita's approach to a broader class of nonlinear parabolic equations.

## Key findings

- Blowup occurs under specific Morrey space norm conditions.
- The criterion complements existing global existence conditions.
- Method extends Fujita's approach to other nonlinear equations.

## Abstract

This note is devoted to a simple proof of blowup of solutions for a nonlinear heat equation. The criterion for a blowup is expressed in terms of a Morrey space norm and is in a sense complementary to conditions guaranteeing the global in time existence of solutions. The method goes back to H. Fujita and extends to other nonlinear parabolic equations.