THE GLOBAL UNIQUENESS OF A DISSIPATIVE FRACTIONAL HELMHOLTZ EQUATION

In this paper, we consider the Dirichlet problem of the fractional Helmholtz equation with dissipation, as well as study the inverse problem of determining the source function, potential function and dissipation of the equation by Dirichlet to Neumann (DtN) map and Runge approximation. We prove the global uniqueness of the three functions of the equation under low-frequency conditions. As the main result, it implies that one can use the external data to uniquely recover the unknown function of the equation in low-frequency case, and will be of important significance in photoacoustic tomography and thermoacoustic tomography.