# On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis

## TL;DR

This paper proves the existence of an exponential attractor for a class of coupled PDEs modeling biomass spreading with degenerate diffusion and chemotaxis, under specific balance conditions, contributing to understanding long-term dynamics.

## Contribution

It establishes the existence of exponential and finite-dimensional global attractors for PDEs with degenerate diffusion and chemotaxis, under new balance conditions.

## Key findings

- Existence of an exponential attractor for the PDE class.
- Finite-dimensional global attractor under certain conditions.
- Conditions linking degeneracy and chemotactic growth are identified.

## Abstract

In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We show the existence of an exponential attractor and, hence, of a finite-dimensional global attractor under certain 'balance conditions' on the order of the degeneracy and the growth of the chemotactic function.