Integral and Variational Formulations for the Helmholtz Equation Inverse Source Problem

الملخص EN

The purpose of this paper is to explore the Hilbert space functional structure of the Helmholtz equation inverse source problem.

An integral equation for the sources reconstruction based on the composition of the trace and Green's function operators is introduced and compared with the reciprocity source reconstruction methodologies.

An equivalence theorem comparing the integral inverse source equation with the variational weak reciprocity gap functional equation is then demonstrated.

Some examples on applications to the unitary disk are presented.