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.
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.
Impact and interest:
Citation counts are sourced monthly from and citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.
|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|
Repository Staff Only: item control page