Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
MC 5417
Basel Jayyusi | Applied Mathematics, University of Waterloo
A geometric investigation of non-regular separation applied to the bi-Helmholtz equation & it's connection to symmetry operators
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 $\mathbb{R}^2$ but does not admit non-trivial non-regular separation in the parabolic and elliptic-hyperbolic coordinate systems of $\mathbb{R}^2$. 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.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
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