# On a class of reaction-diffusion equations with aggregation

## TL;DR

This paper investigates a class of reaction-diffusion equations related to aggregation phenomena, establishing conditions for global existence, blow-up, steady-state properties, and stability of equilibria.

## Contribution

It provides new results on existence, blow-up, and stability for reaction-diffusion equations modeling aggregation, including chemotaxis, with analysis of steady states.

## Key findings

- Global existence and blow-up criteria established.
- Properties of steady-state solutions analyzed.
- Stability of constant equilibria studied.

## Abstract

In this paper, global-in-time existence and blow up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria and the non-existence of non-constant solutions are studied in certain cases.