Existence of travelling wave solutions for a model of tumour invasion
Data(s) |
2014
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Resumo |
The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed. |
Formato |
application/pdf |
Identificador | |
Publicador |
Society for Industrial and Applied Mathematics |
Relação |
http://eprints.qut.edu.au/67124/1/092312R.pdf http://epubs.siam.org/doi/abs/10.1137/130923129 DOI:10.1137/130923129 Harley, K., van Heijster, P., Marangell, R., Pettet, G.J., & Wechselberger, M. (2014) Existence of travelling wave solutions for a model of tumour invasion. SIAM Journal Applied Dynamical Systems, 13(1), pp. 366-396. |
Direitos |
Copyright 2014 Society for Industrial and Applied Mathematics |
Fonte |
School of Mathematical Sciences |
Palavras-Chave | #010110 Partial Differential Equations #010202 Biological Mathematics #010204 Dynamical Systems in Applications #advection-reaction-diffusion systems #canards #singularly perturbed systems #travelling wave solutions |
Tipo |
Journal Article |