Identification of the Point Sources in Some Stochastic Wave Equations

Identification of the Point Sources in Some Stochastic Wave Equations

We introduce and study a type of (one-dimensional) wave equations with noisy point sources. We first study the existence and uniqueness problem of the equations. Then, we assume that the locations of point sources are unknown but we can observe the solution at some other location continuously in tim...

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Main Authors: Yaozhong Hu, Guanglin Rang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/219876
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spelling doaj-4a9394ab0d78484a9182594da521bf632020-11-24T22:32:39ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/219876219876Identification of the Point Sources in Some Stochastic Wave EquationsYaozhong Hu0Guanglin Rang1Department of Mathematics, University of Kansas, Lawrence, KS 66045, USASchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaWe introduce and study a type of (one-dimensional) wave equations with noisy point sources. We first study the existence and uniqueness problem of the equations. Then, we assume that the locations of point sources are unknown but we can observe the solution at some other location continuously in time. We propose an estimator to identify the point source locations and prove the convergence of our estimator.http://dx.doi.org/10.1155/2014/219876
collection DOAJ
language English
format Article
sources DOAJ
author Yaozhong Hu
Guanglin Rang
spellingShingle Yaozhong Hu
Guanglin Rang
Identification of the Point Sources in Some Stochastic Wave Equations
Abstract and Applied Analysis
author_facet Yaozhong Hu
Guanglin Rang
author_sort Yaozhong Hu
title Identification of the Point Sources in Some Stochastic Wave Equations
title_short Identification of the Point Sources in Some Stochastic Wave Equations
title_full Identification of the Point Sources in Some Stochastic Wave Equations
title_fullStr Identification of the Point Sources in Some Stochastic Wave Equations
title_full_unstemmed Identification of the Point Sources in Some Stochastic Wave Equations
title_sort identification of the point sources in some stochastic wave equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We introduce and study a type of (one-dimensional) wave equations with noisy point sources. We first study the existence and uniqueness problem of the equations. Then, we assume that the locations of point sources are unknown but we can observe the solution at some other location continuously in time. We propose an estimator to identify the point source locations and prove the convergence of our estimator.
url http://dx.doi.org/10.1155/2014/219876
work_keys_str_mv AT yaozhonghu identificationofthepointsourcesinsomestochasticwaveequations
AT guanglinrang identificationofthepointsourcesinsomestochasticwaveequations
_version_ 1725733013733507072

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