A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source

TL;DR

This paper establishes explicit conditions ensuring uniform boundedness of solutions in a 2D chemotaxis-haptotaxis model, improving upon previous results by including a broad class of cell sources.

Contribution

It provides a new explicit criterion involving chemotactic strength, damping rate, and initial cell mass for boundedness in a 2D chemotaxis-haptotaxis system with various sources.

Findings

Explicit boundedness condition derived

Improves existing 2D global existence results

Applicable to models with zero or sub-logistic sources

Abstract

We consider the Neumann problem for a coupled chemotaxis-haptotaxis model of cancer invasion with/without kinetic source in a 2D bounded and smooth domain. For a large class of cell kinetic sources including zero source and sub-logistic sources, we detect an explicit condition involving the chemotactic strength, the asymptotic "damping" rate, and the initial mass of cells to ensure uniform-in-time boundedness for the corresponding Neumann problem. Our finding significantly improves existing 2D global existence and boundedness in related chemotaxis-/haptotaxis systems.