Localised structures in some non-standard, singularly perturbed partial differential equations
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Paige Davis Thesis
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Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. |
Description
This thesis addresses the existence and stability of localised solutions in some nonstandard systems of partial differential equations. In particular, it locates the linearised spectrum of a Keller-Segel model for bacterial chemotaxis with logarithmic chemosensitivity, establishes the existence of travelling wave solutions to the Gatenby-Gawlinski model for tumour invasion with the acid-mediation hypothesis using geometric singular perturbation theory, and formulates the Evans function for a trivial defect solution in a general reaction diffusion equation with an added heterogeneous defect. Extending the analysis to these non-standard problems provides a foundation and insight for more general dynamical systems.
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| ID Code: | 201835 |
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| Item Type: | QUT Thesis (PhD) |
| Supervisor: | van Heijster, Petrus, McCue, Scott, & Marangell, Robert |
| Keywords: | Stationary solutions, Travelling wave solutions, Linearised operators, Essential Spectrum, Absolute Spectrum, Point Spectrum, Geometric Singular Perturbation Theory, Heterogeneous equations, Jump-type defect, Evans Function |
| DOI: | 10.5204/thesis.eprints.201835 |
| Divisions: | Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Schools > School of Mathematical Sciences |
| Institution: | Queensland University of Technology |
| Deposited On: | 23 Jul 2020 22:33 |
| Last Modified: | 23 Jul 2020 22:33 |
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