A non-local reaction advection-diffusion model for self-interacting species
| dc.contributor.author | Yue, Zongzhi | |
| dc.contributor.supervisor | Lewis, Mark | |
| dc.contributor.supervisor | Ibrahim, Slim | |
| dc.date.accessioned | 2024-08-26T20:36:11Z | |
| dc.date.available | 2024-08-26T20:36:11Z | |
| dc.date.issued | 2024 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science MSc | |
| dc.description.abstract | In biological models, advection is inherently a non-local process. In this thesis, we proposed a natural extension of the non-local advection-diffusion model in [7] to include the reaction term (birth and death process). This thesis begins with an investigation of the well-posedness and existence of travelling wave solutions for this non-local reaction-advection-diffusion (RAD) equation. We prove the local-in-time existence and positivity of solutions under H³(R) initial conditions and provide a continuation criterion of the equation. Subsequently, we explore the existence of travelling wave solutions of this non-local RAD using a combination of perturbation methods, Fredholm operator theory, and Banach's fixed point theorem. Our analysis reveals that such solutions exist when the non-local advection term is small. Finally, we simulate the travelling wave solution to verify our theoretical findings and speculate the solution with a large advection term. | |
| dc.description.scholarlevel | Graduate | |
| dc.identifier.uri | https://hdl.handle.net/1828/20307 | |
| dc.language | English | eng |
| dc.language.iso | en | |
| dc.rights | Available to the World Wide Web | |
| dc.subject | reaction-advection-diffusion | |
| dc.subject | non-local advection | |
| dc.subject | existence theorems | |
| dc.subject | mathematical ecology | |
| dc.subject | travelling wave solutions | |
| dc.title | A non-local reaction advection-diffusion model for self-interacting species | |
| dc.type | Thesis |