Improvements and generalizations of results concerning attraction-repulsion chemotaxis models

TL;DR

This paper reviews and enhances recent results on nonlinear and linear chemotaxis models with chemoattractant and chemorepellent, providing generalized findings, sharper claims, and extending to models with logistic sources.

Contribution

It generalizes and improves existing results on chemotaxis models, unifies claims, and extends analysis to include logistic source terms.

Findings

Generalized previous chemotaxis model results

Established sharper mathematical claims

Extended analysis to models with logistic sources

Abstract

We enter the details of two recent articles concerning as many chemotaxis models, one nonlinear and the other linear, and both with produced chemoattractant and saturated chemorepellent. These works, when properly analyzed, leave open room for some improvement of their results. We generalize the outcomes of the mentioned articles, establish other statements and put all the claims together; in particular, we select the sharpest ones and schematize them. Moreover, we complement our research also when logistic sources are considered in the overall study.