# American Institute of Mathematical Sciences

• Previous Article
Reconstruction of perfectly conducting rough surfaces by the use of inhomogeneous surface impedance modeling
• IPI Home
• This Issue
• Next Article
A time-domain probe method for three-dimensional rough surface reconstructions
May  2009, 3(2): 275-294. doi: 10.3934/ipi.2009.3.275

## Full identification of acoustic sources with multiple frequencies and boundary measurements

 1 CEMAT-IST, Departamento de Matemática, Instituto Superior Técnico (TULisbon), Avenida Rovisco Pais, 1049-001 Lisboa, Portugal 2 CEMAT-IST and Departamento de Matemática, Faculdade de Ciências e Tecnologia (NULisbon), Universidade Nova de Lisboa, Quinta da Torre, Caparica, Portugal 3 Programa de Engenharia Nuclear, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

Received  December 2008 Revised  March 2009 Published  May 2009

In this paper we study the identification of acoustic sources in a domain $\Omega$ from boundary data. With a single frequency, we show that identification is possible if, besides the boundary data, considerable information regarding the type of the source is considered. For the general case, we present an identification result using multiple frequencies and boundary measurements. We show that for compactly supported sources in $\Omega$, the completion of Cauchy data has at most one solution and thus for this type of sources, identification is possible using variable frequencies and incomplete boundary measurements. A numerical method based on the reciprocity functional is proposed and tested for several numerical examples. For compact sources, a data completion method is proposed and tested in order to apply the previous method.
Citation: Carlos J. S. Alves, Nuno F. M. Martins, Nilson C. Roberty. Full identification of acoustic sources with multiple frequencies and boundary measurements. Inverse Problems and Imaging, 2009, 3 (2) : 275-294. doi: 10.3934/ipi.2009.3.275
 [1] Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems and Imaging, 2007, 1 (4) : 643-660. doi: 10.3934/ipi.2007.1.643 [2] Roland Griesmaier. Reciprocity gap music imaging for an inverse scattering problem in two-layered media. Inverse Problems and Imaging, 2009, 3 (3) : 389-403. doi: 10.3934/ipi.2009.3.389 [3] Fang Zeng, Xiaodong Liu, Jiguang Sun, Liwei Xu. The reciprocity gap method for a cavity in an inhomogeneous medium. Inverse Problems and Imaging, 2016, 10 (3) : 855-868. doi: 10.3934/ipi.2016024 [4] P. Álvarez-Caudevilla, J. D. Evans, V. A. Galaktionov. The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 807-827. doi: 10.3934/dcds.2015.35.807 [5] Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems and Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469 [6] Jianli Xiang, Guozheng Yan. The uniqueness of the inverse elastic wave scattering problem based on the mixed reciprocity relation. Inverse Problems and Imaging, 2021, 15 (3) : 539-554. doi: 10.3934/ipi.2021004 [7] Shuli Chen, Zewen Wang, Guolin Chen. Cauchy problem of non-homogenous stochastic heat equation and application to inverse random source problem. Inverse Problems and Imaging, 2021, 15 (4) : 619-639. doi: 10.3934/ipi.2021008 [8] Lekbir Afraites, Chorouk Masnaoui, Mourad Nachaoui. Shape optimization method for an inverse geometric source problem and stability at critical shape. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 1-21. doi: 10.3934/dcdss.2021006 [9] Lorena Bociu, Petronela Radu. Existence of weak solutions to the Cauchy problem of a semilinear wave equation with supercritical interior source and damping. Conference Publications, 2009, 2009 (Special) : 60-71. doi: 10.3934/proc.2009.2009.60 [10] Zhousheng Ruan, Sen Zhang, Sican Xiong. Solving an inverse source problem for a time fractional diffusion equation by a modified quasi-boundary value method. Evolution Equations and Control Theory, 2018, 7 (4) : 669-682. doi: 10.3934/eect.2018032 [11] Loc H. Nguyen, Qitong Li, Michael V. Klibanov. A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media. Inverse Problems and Imaging, 2019, 13 (5) : 1067-1094. doi: 10.3934/ipi.2019048 [12] Jianliang Li, Jiaqing Yang, Bo Zhang. A linear sampling method for inverse acoustic scattering by a locally rough interface. Inverse Problems and Imaging, 2021, 15 (5) : 1247-1267. doi: 10.3934/ipi.2021036 [13] Xiaoli Feng, Meixia Zhao, Peijun Li, Xu Wang. An inverse source problem for the stochastic wave equation. Inverse Problems and Imaging, 2022, 16 (2) : 397-415. doi: 10.3934/ipi.2021055 [14] Kazuhiro Ishige. On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data. Discrete and Continuous Dynamical Systems, 1995, 1 (4) : 521-546. doi: 10.3934/dcds.1995.1.521 [15] Brian Sleeman. The inverse acoustic obstacle scattering problem and its interior dual. Inverse Problems and Imaging, 2009, 3 (2) : 211-229. doi: 10.3934/ipi.2009.3.211 [16] Yavar Kian, Morgan Morancey, Lauri Oksanen. Application of the boundary control method to partial data Borg-Levinson inverse spectral problem. Mathematical Control and Related Fields, 2019, 9 (2) : 289-312. doi: 10.3934/mcrf.2019015 [17] Michael V. Klibanov, Dinh-Liem Nguyen, Loc H. Nguyen, Hui Liu. A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data. Inverse Problems and Imaging, 2018, 12 (2) : 493-523. doi: 10.3934/ipi.2018021 [18] Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042 [19] Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, Lam Nguyen. A globally convergent numerical method for a 1-d inverse medium problem with experimental data. Inverse Problems and Imaging, 2016, 10 (4) : 1057-1085. doi: 10.3934/ipi.2016032 [20] Michael V. Klibanov, Thuy T. Le, Loc H. Nguyen, Anders Sullivan, Lam Nguyen. Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2021068

2020 Impact Factor: 1.639

## Metrics

• PDF downloads (103)
• HTML views (0)
• Cited by (23)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]