Some properties of Bessel functions with applications to Neumann eigenvalues in the unit disc
(2013) In Bachelor's Theses in Mathematical Sciences MATK01 20122Mathematics (Faculty of Sciences)
- Abstract
- A study is made of the multiplicities of the eigenvalues of the Laplace operator in the unit disc with Neumann boundary conditions. Our result is that all eigenvalues are simple or double, a result which is well-known if one instead considers Dirichlet boundary conditions. The result is proved by using some properties of Bessel functions. We also give an application to standing water waves in a cylinder.
- Popular Abstract (Swedish)
- Vi studerar multipliciteten av egenvärdena till Laplace-operatorn i enhetsskivan med Neumann-randvillkor. Vårt resultat är att alla egenvärden är enkla eller dubbla, ett resultat som är välkänt om man istället föreskriver Dirichlet-randvillkor. Beviset bygger på några egenskaper hos Besselfunktioner. Vi ger också en tillämpning på stående vattenvågor i en cylinder.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/7370411
- author
- Ashu, Ashu Mathias LU
- supervisor
-
- Erik Wahlén LU
- organization
- course
- MATK01 20122
- year
- 2013
- type
- M2 - Bachelor Degree
- subject
- keywords
- Bessel functions, Neumann eigenvalues, Bourget's hypothesis, unit disc, standing water waves
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4021-2013
- ISSN
- 1654-6229
- other publication id
- 2013:K1
- language
- English
- id
- 7370411
- date added to LUP
- 2015-06-18 11:15:15
- date last changed
- 2015-12-21 15:18:41
@misc{7370411, abstract = {{A study is made of the multiplicities of the eigenvalues of the Laplace operator in the unit disc with Neumann boundary conditions. Our result is that all eigenvalues are simple or double, a result which is well-known if one instead considers Dirichlet boundary conditions. The result is proved by using some properties of Bessel functions. We also give an application to standing water waves in a cylinder.}}, author = {{Ashu, Ashu Mathias}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Some properties of Bessel functions with applications to Neumann eigenvalues in the unit disc}}, year = {{2013}}, }