A geometric investigation of non-regular separation applied to the bi-Helmholtz equation & its connection to symmetry operators
| dc.contributor.author | Jayyusi, Basel | |
| dc.date.accessioned | 2024-05-23T14:54:10Z | |
| dc.date.available | 2024-05-23T14:54:10Z | |
| dc.date.issued | 2024-05-23 | |
| dc.date.submitted | 2024-05-13 | |
| dc.description.abstract | The theory of non-regular separation is examined in its geometric form and applied to the bi-Helmholtz equation in the flat coordinate systems in 2-dimensions. It is shown that the bi-Helmholtz equation does not admit regular separation in any dimensions on any Riemannian manifold. It is demonstrated that the bi-Helmholtz equation admits non-trivial non-regular separation in the Cartesian and polar coordinate systems in R^2 but does not admit non-trivial non-regular separation in the parabolic and elliptic-hyperbolic coordinate systems of R^2. The results are applied to the study of small vibrations of a thin solid circular plate. It is conjectured that the reason as to why non-trivial non-regular separation occurs in the Cartesian and polar coordinate systems is due to the existence of first order symmetries (Killing vectors) in those coordinate systems. Symmetries of the bi-Helmholtz equation are examined in detail giving supporting evidence of the conjecture. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/20585 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | mathematical physics | en |
| dc.subject | partial differential equations | en |
| dc.subject | separation of variables | en |
| dc.subject | differential geometry | en |
| dc.subject | symmetries | en |
| dc.title | A geometric investigation of non-regular separation applied to the bi-Helmholtz equation & its connection to symmetry operators | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Applied Mathematics | en |
| uws-etd.degree.discipline | Applied Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Jayyusi, Basel | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |