Analysis of a model arising from invasion by precursor and differentiated cells

TL;DR

This paper analyzes wave solutions in a reaction-diffusion model related to cell invasion, establishing conditions for existence, monotonicity, and uniqueness of these solutions.

Contribution

It provides new mathematical insights into the existence and properties of wave solutions in a degenerated reaction-diffusion system modeling cell invasion.

Findings

Existence of wave solutions for speeds above a critical threshold

Non-existence of monotonic waves below this threshold

Characterization of wave monotonicity, uniqueness, and asymptotic behavior

Abstract

We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. We show that there exists a family of waves for the wave speed larger than or equals a certain number, and below which there is no monotonic wave solutions. We also investigate the monotonicity, uniqueness and asymptotics of the waves.