Travelling waves in a free boundary mechanobiological model of an epithelial tissue

Author: 

Murphy, R
Buenzli, P
Baker, R
Simpson, M

Publication Date: 

1 January 2021

Journal: 

Applied Mathematics Letters

Last Updated: 

2021-06-12T03:48:02.78+01:00

Volume: 

111

DOI: 

10.1016/j.aml.2020.106636

abstract: 

© 2020 Elsevier Ltd We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse travelling wave solutions with negative, zero, and positive wavespeeds. Unlike classical travelling wave solutions of reaction–diffusion equations, the travelling wave solutions that we explore have a well-defined front and are not associated with a heteroclinic orbit in the phase plane. We find leading order expressions for both the wavespeed and the density at the free boundary. Interestingly, whether the travelling wave solution invades or retreats depends only on whether the carrying capacity density corresponds to cells being in compression or extension.

Symplectic id: 

1109569

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article