### Electronic Research Archive

2020, Issue 3: 1239-1255. doi: 10.3934/era.2020068
Special Issues

# On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements

• Received: 01 May 2020 Revised: 01 June 2020
• Primary: 35Q60, 35J05, 31B10; Secondary: 35R30, 78A40

• We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.

Citation: Xiaoping Fang, Youjun Deng, Wing-Yan Tsui, Zaiyun Zhang. On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements[J]. Electronic Research Archive, 2020, 28(3): 1239-1255. doi: 10.3934/era.2020068

### Related Papers:

• We consider a particular type of inverse problems where an unknown source embedded in an inhomogeneous medium, and one intends to recover the source and/or the medium by knowledge of the wave field (generated by the unknown source) outside the medium. This type of inverse problems arises in many applications of practical importance, including photoacoustic and thermoacoustic tomography, brain imaging and geomagnetic anomaly detections. We survey the recent mathematical developments on this type of inverse problems. We discuss the mathematical tools developed for effectively tackling this type of inverse problems. We also discuss a related inverse problem of recovering an embedded obstacle and its surrounding medium by active measurements.

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