Inverse Problems and Imaging (IPI)

Increasing stability for the inverse source scattering problem with multi-frequencies

Pages: 745 - 759, Volume 11, Issue 4, August 2017      doi:10.3934/ipi.2017035

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Peijun Li - Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States (email)
Ganghua Yuan - KLAS, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, China (email)

Abstract: Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source scattering problem which is to reconstruct the source function. Our results show that increasing stability can be obtained for the inverse problem by using only the Dirichlet boundary data with multi-frequencies.

Keywords:  Stability, multi-frequencies, inverse source problem, Helmholtz equation, partial differential equation.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 78A46.

Received: July 2016;      Revised: March 2017;      Available Online: June 2017.