• Previous Article
    A time-domain probe method for three-dimensional rough surface reconstructions
  • IPI Home
  • This Issue
  • Next Article
    Reconstruction of perfectly conducting rough surfaces by the use of inhomogeneous surface impedance modeling
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 & 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 & 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 & Imaging, 2009, 3 (3) : 389-403. doi: 10.3934/ipi.2009.3.389

[3]

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 & Continuous Dynamical Systems - A, 2015, 35 (3) : 807-827. doi: 10.3934/dcds.2015.35.807

[4]

Fang Zeng, Xiaodong Liu, Jiguang Sun, Liwei Xu. The reciprocity gap method for a cavity in an inhomogeneous medium. Inverse Problems & Imaging, 2016, 10 (3) : 855-868. doi: 10.3934/ipi.2016024

[5]

Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469

[6]

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

[7]

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 & Control Theory, 2018, 7 (4) : 669-682. doi: 10.3934/eect.2018032

[8]

Brian Sleeman. The inverse acoustic obstacle scattering problem and its interior dual. Inverse Problems & Imaging, 2009, 3 (2) : 211-229. doi: 10.3934/ipi.2009.3.211

[9]

Kazuhiro Ishige. On the existence of solutions of the Cauchy problem for porous medium equations with radon measure as initial data. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 521-546. doi: 10.3934/dcds.1995.1.521

[10]

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 & Imaging, 2018, 12 (2) : 493-523. doi: 10.3934/ipi.2018021

[11]

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 & Imaging, 2016, 10 (4) : 1057-1085. doi: 10.3934/ipi.2016032

[12]

Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems & Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042

[13]

Yavar Kian, Morgan Morancey, Lauri Oksanen. Application of the boundary control method to partial data Borg-Levinson inverse spectral problem. Mathematical Control & Related Fields, 2019, 9 (2) : 289-312. doi: 10.3934/mcrf.2019015

[14]

Fioralba Cakoni, Rainer Kress. Integral equations for inverse problems in corrosion detection from partial Cauchy data. Inverse Problems & Imaging, 2007, 1 (2) : 229-245. doi: 10.3934/ipi.2007.1.229

[15]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271

[16]

Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems & Imaging, 2011, 5 (2) : 297-322. doi: 10.3934/ipi.2011.5.297

[17]

Victor Isakov. On uniqueness in the inverse conductivity problem with local data. Inverse Problems & Imaging, 2007, 1 (1) : 95-105. doi: 10.3934/ipi.2007.1.95

[18]

Guanghui Hu, Andreas Kirsch, Tao Yin. Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves. Inverse Problems & Imaging, 2016, 10 (1) : 103-129. doi: 10.3934/ipi.2016.10.103

[19]

Peijun Li, Ganghua Yuan. Increasing stability for the inverse source scattering problem with multi-frequencies. Inverse Problems & Imaging, 2017, 11 (4) : 745-759. doi: 10.3934/ipi.2017035

[20]

Kenichi Sakamoto, Masahiro Yamamoto. Inverse source problem with a final overdetermination for a fractional diffusion equation. Mathematical Control & Related Fields, 2011, 1 (4) : 509-518. doi: 10.3934/mcrf.2011.1.509

2018 Impact Factor: 1.469

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (18)

[Back to Top]