Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth (Advances in Applied Mathematics and Mechanics, 2018)
Mass migration of cells (via wave motion) plays an important role in manybiological processes, particularly chemotaxis. We study the existence of travellingwave solutions for a chemotaxis model on a microscopic scale. The interaction betweennutrients and chemoattractants are considered. Unlike previous approaches,we allow for diffusion of substrates, degradation of chemoattractants and cell growth(constant and linear growth rate). We apply asymptotic methods to investigate thebehaviour of the solutions when cells are highly sensitive to extracellular signalling.Explicit solutions are demonstrated, and their biological implications are presented.The results presented here extend and generalize known results.