Spectral Analysis for a Wave/Plate Transmission System
We are concerned with the transmission system of a 1D damped wave equation and a 1D undamped plate equation. Our result reads as follows: the spectrum of the infinitesimal generator of the semigroup associated with the system in question consists merely of an infinite sequence of eigenvalues which a...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/7849561 |
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| author | Chengqiang Wang |
| author_facet | Chengqiang Wang |
| author_sort | Chengqiang Wang |
| collection | DOAJ |
| description | We are concerned with the transmission system of a 1D damped wave equation and a 1D undamped plate equation. Our result reads as follows: the spectrum of the infinitesimal generator of the semigroup associated with the system in question consists merely of an infinite sequence of eigenvalues which are all located in the open left half of the complex plane; the sequence of eigenvalues has the imaginary axis and another vertical line to the left of the imaginary axis as its asymptote lines; the energy of the system under consideration decreases to zero as time goes to infinity. |
| format | Article |
| id | doaj-art-d0b8f3c79de542e78f03e0b43d033921 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d0b8f3c79de542e78f03e0b43d0339212025-02-03T05:53:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/78495617849561Spectral Analysis for a Wave/Plate Transmission SystemChengqiang Wang0School of Mathematics, Chengdu Normal University, Chengdu 611130, ChinaWe are concerned with the transmission system of a 1D damped wave equation and a 1D undamped plate equation. Our result reads as follows: the spectrum of the infinitesimal generator of the semigroup associated with the system in question consists merely of an infinite sequence of eigenvalues which are all located in the open left half of the complex plane; the sequence of eigenvalues has the imaginary axis and another vertical line to the left of the imaginary axis as its asymptote lines; the energy of the system under consideration decreases to zero as time goes to infinity.http://dx.doi.org/10.1155/2019/7849561 |
| spellingShingle | Chengqiang Wang Spectral Analysis for a Wave/Plate Transmission System Advances in Mathematical Physics |
| title | Spectral Analysis for a Wave/Plate Transmission System |
| title_full | Spectral Analysis for a Wave/Plate Transmission System |
| title_fullStr | Spectral Analysis for a Wave/Plate Transmission System |
| title_full_unstemmed | Spectral Analysis for a Wave/Plate Transmission System |
| title_short | Spectral Analysis for a Wave/Plate Transmission System |
| title_sort | spectral analysis for a wave plate transmission system |
| url | http://dx.doi.org/10.1155/2019/7849561 |
| work_keys_str_mv | AT chengqiangwang spectralanalysisforawaveplatetransmissionsystem |