Global dynamics of chemotaxis-consumption systems with oppositely acting nonlocal terms

TL;DR

This paper analyzes a chemotaxis system with local and nonlocal source terms, establishing conditions for global existence and boundedness of solutions, and exploring how reaction term variations affect long-term dynamics.

Contribution

It extends previous models by considering more general source terms and their impact on solution boundedness and system behavior.

Findings

Conditions for global existence of solutions.

Identification of source term structures that prevent cell aggregation.

Impact of reaction term variations on long-term dynamics.

Abstract

This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on conditions under which solutions exist for all time and remain uniformly bounded, preventing cell aggregation. Two types of source terms are considered. In the first case, the structure of the source term ensures that the total cell mass remains controlled over time. In the second case, this mass control is not guaranteed, which can lead to different dynamic behaviors. The results extend previous studies that examined similar systems but with more specific source terms and slightly different chemical dynamics. This work highlights how variations in the reaction terms influence the long-term behavior of the system.