On increasing stability in an inverse source problem with local boundary data at many wave numbers

ABSTRACT

To derive the increasing stability of the source term in the Helmholtz equation from local boundary data, we utilize sharp bounds of the analytic continuation for higher wave numbers, the Huygens' principle, and bounds in the lateral Cauchy problem for the wave equation.

Keywords:

• Inverse source problems
• Helmholtz equation
• increasing stability

2010 Mathematics Subject Classification:

• 35R30

Acknowledgments

This research is supported in part by the Emylou Keith and Betty Dutcher Distinguished Professorship and the NSF grant DMS 15-14886.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is supported in part by the Emylou Keith and Betty Dutcher Distinguished Professorship and the NSF (grant number DMS 15-14886).