The inverse scattering problem for a partially coated penetrable cavity with interior measurements

Abstract

In this paper we consider the inverse scattering problem for a cavity that is bounded by a partially coated penetrable inhomogeneous medium of compact support and recover the shape of the cavity and the surface conductivity from a knowledge of measured scattered waves due to point sources located on a curve or surface inside the cavity. First, we prove that both the shape of the cavity and the surface conductivity on the coated part can be uniquely determined from a knowledge of the measured data. Next, we establish a linear sampling method for determining both the shape of the cavity and the surface conductivity. A central role in our justification is played by an eigenvalue problem which we call the exterior transmission eigenvalue problem. Finally, we present some numerical examples to illustrate the validity of our method.

Keywords:

• Inverse scattering
• surface conductivity
• exterior transmission eigenvalues
• interior measurements
• linear sampling method

AMS Subject Classifications:

• 35R30
• 65F22
• 65R20
• 65R32

Acknowledgements

This work was done while the author was visiting the Department of Mathematical Sciences in University of Delaware as a Post-Doctoral researcher and its hospitality is deeply acknowledged. Special thanks are due to Professor Fioralba Cakoni for her useful discussions on this project.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The research is supported in part by the National Natural Science Foundation of China [grant number 11426052]; the Program of Chongqing Education Commission [grant number KJ1400522] and the Program of Chongqing Innovation Team Project in University [grant number KJTD201308].