Canards in advection-reaction-diffusion systems in one spatial dimension

Harley, Kristen E. (2014) Canards in advection-reaction-diffusion systems in one spatial dimension. PhD by Publication, Queensland University of Technology.

Abstract

This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions.

The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.

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34 since deposited on 16 Feb 2015
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ID Code: 79261
Item Type: QUT Thesis (PhD by Publication)
Supervisor: Pettet, Graeme & van Heijster, Petrus
Keywords: canards, geometric singular perturbation theory, travelling waves, advection-reaction-diffusion models, mathematical biology
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Institution: Queensland University of Technology
Deposited On: 16 Feb 2015 06:24
Last Modified: 14 Nov 2015 14:01

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