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

Abstract:

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 or...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.aml.2020.106636

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-6304-9333
Publisher:
Elsevier
Journal:
Applied Mathematics Letters More from this journal
Volume:
111
Article number:
106636
Publication date:
2020-07-22
Acceptance date:
2020-07-14
DOI:
EISSN:
1873-5452
ISSN:
0893-9659
Language:
English
Keywords:
Pubs id:
1109569
Local pid:
pubs:1109569
Deposit date:
2020-08-14

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