The inverse source problem for the Helmholtz equation is studied. An unknown source is to be identified from the knowledge of its radiated wave. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, we prove that data obtained from finitely many frequencies is not sufficient. On the other hand, if the frequency varies within an open interval of the positive real line, then the source is determined uniquely. An algorithm is based on an incomplete Fourier transform of the measured data and we establish an error estimate under certain regularity assumptions on the source function. We conclude that multi-frequency data not only leads to uniqueness for the inverse source problem, but in fact it contributes with a stability result for the reconstruction of an unknown source.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Acosta, Sebastian Ignacio, "A Multi-Frequency Inverse Source Problem for the Helmholtz Equation" (2011). Theses and Dissertations. 2511.
Inverse source problem, Helmholtz equation, multi-frequency