Recovery of interior eigenvalues from reduced near field data

Abstract

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The domain can be arbitrarily small but fixed.The scattered waves are measured on the same surface. An effective procedure is suggested for recovery of interior eigenvalues by these data.

Keywords:

• Partial scattering data
• inverse scattering problem
• scattering by an obstacle
• interior transmission eigenvalues

AMS Subject Classifications:

• 35P25
• 65N21
• 78A46

Acknowledgements

The authors are thankful to Rakesh, D. Colton and A. Lechleiter for useful discussions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications and the Portuguese Foundation for Science and Technology (“FCT–Fundção para a Ciência e a Tecnologia”), within project [PEst-OE/MAT/UI4106/2014]; partially supported by the NSF [grant number DMS-1410547].