Spectral Analysis for a Wave/Plate Transmission System

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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Main Author: Chengqiang Wang
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2019/7849561
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spelling doaj-d0b8f3c79de542e78f03e0b43d0339212021-07-02T18:03:02ZengHindawi LimitedAdvances 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
collection DOAJ
language English
format Article
sources DOAJ
author Chengqiang Wang
spellingShingle Chengqiang Wang
Spectral Analysis for a Wave/Plate Transmission System
Advances in Mathematical Physics
author_facet Chengqiang Wang
author_sort Chengqiang Wang
title Spectral Analysis for a Wave/Plate Transmission System
title_short 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_sort spectral analysis for a wave/plate transmission system
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2019-01-01
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.
url http://dx.doi.org/10.1155/2019/7849561
work_keys_str_mv AT chengqiangwang spectralanalysisforawaveplatetransmissionsystem
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