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| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2000
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/math/0012113 |
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| _version_ | 1866915559977779200 |
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| author | Aslanyan, A. Davies, E. B. |
| author_facet | Aslanyan, A. Davies, E. B. |
| contents | We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the Fourier decomposition method. The ODE system obtained in this way is then solved numerically yielding the eigenvalues of the operator. The same approach allows us to find complex resonances arising in some non-compact domains. We discuss numerical examples related to quantum waveguide problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0012113 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Separation of variables in perturbed cylinders Aslanyan, A. Davies, E. B. Spectral Theory Numerical Analysis 34L05, 34L40, 35P05, 47A75, 65L15 We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the Fourier decomposition method. The ODE system obtained in this way is then solved numerically yielding the eigenvalues of the operator. The same approach allows us to find complex resonances arising in some non-compact domains. We discuss numerical examples related to quantum waveguide problems. |
| title | Separation of variables in perturbed cylinders |
| topic | Spectral Theory Numerical Analysis 34L05, 34L40, 35P05, 47A75, 65L15 |
| url | https://arxiv.org/abs/math/0012113 |