Logistic damping effect in chemotaxis models with density-suppressed motility

TL;DR

This paper investigates a chemotaxis model with density-dependent motility and logistic growth, analyzing how logistic damping influences the global boundedness and long-term behavior of solutions in bounded domains.

Contribution

It establishes minimal conditions under which logistic damping ensures global boundedness and describes the asymptotic behavior of solutions in chemotaxis models.

Findings

Logistic damping can guarantee global boundedness under minimal conditions.

Solutions exhibit specific asymptotic behavior influenced by logistic damping.

The model extends understanding of chemotaxis with density-suppressed motility.

Abstract

This paper is concerned with a parabolic-elliptic chemotaxis model with density-suppressed motility and general logistic source in an $n$-dimensional smooth bounded domain with Neumann boundary conditions. Under the minimal conditions for the density-suppressed motility function, we explore how strong the logistic damping can warrant the global boundedness of solutions, and further establish the asymptotic behavior of solutions on top of the conditions.