Canards in advection-reaction-diffusion systems in one spatial dimension
Data(s) |
2014
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Publicador |
Queensland University of Technology |
Relação |
http://eprints.qut.edu.au/79261/1/Kristen_Harley_Thesis.pdf Harley, Kristen E. (2014) Canards in advection-reaction-diffusion systems in one spatial dimension. PhD by Publication, Queensland University of Technology. |
Fonte |
Institute of Health and Biomedical Innovation; School of Mathematical Sciences; Science & Engineering Faculty |
Palavras-Chave | #canards #geometric singular perturbation theory #travelling waves #advection-reaction-diffusion models #mathematical biology |
Tipo |
Thesis |