Hearing the shape of membranes: further results
The spectral function θ(t)=∑m=1∞exp(−tλm), t>0 where {λm}m=1∞ are the eigenvalues of the Laplacian in Rn, n=2 or 3, is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions ∂u∂r+γju=0 on Γj (or Sj), j=1,…,J where Γ...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000825 |
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| _version_ | 1832568322667839488 |
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| author | E. M. E. Zayed |
| author_facet | E. M. E. Zayed |
| author_sort | E. M. E. Zayed |
| collection | DOAJ |
| description | The spectral function θ(t)=∑m=1∞exp(−tλm), t>0 where {λm}m=1∞ are the eigenvalues of the Laplacian in Rn, n=2 or 3, is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions ∂u∂r+γju=0 on Γj (or Sj), j=1,…,J where Γj and Sj, j=1,…,J are parts of the boundaries of these domains respectively, while γj, j=1,…,J are positive constants. |
| format | Article |
| id | doaj-art-e59e818181ae4016a7ca3fafcde8d5d2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e59e818181ae4016a7ca3fafcde8d5d22025-02-03T00:59:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113359159810.1155/S0161171290000825Hearing the shape of membranes: further resultsE. M. E. Zayed0Department of Mathematics, Zagazig University, Faculty of Science, Zagazig, EgyptThe spectral function θ(t)=∑m=1∞exp(−tλm), t>0 where {λm}m=1∞ are the eigenvalues of the Laplacian in Rn, n=2 or 3, is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions ∂u∂r+γju=0 on Γj (or Sj), j=1,…,J where Γj and Sj, j=1,…,J are parts of the boundaries of these domains respectively, while γj, j=1,…,J are positive constants.http://dx.doi.org/10.1155/S0161171290000825 |
| spellingShingle | E. M. E. Zayed Hearing the shape of membranes: further results International Journal of Mathematics and Mathematical Sciences |
| title | Hearing the shape of membranes: further results |
| title_full | Hearing the shape of membranes: further results |
| title_fullStr | Hearing the shape of membranes: further results |
| title_full_unstemmed | Hearing the shape of membranes: further results |
| title_short | Hearing the shape of membranes: further results |
| title_sort | hearing the shape of membranes further results |
| url | http://dx.doi.org/10.1155/S0161171290000825 |
| work_keys_str_mv | AT emezayed hearingtheshapeofmembranesfurtherresults |