The Global Uniqueness Of A Dissipative Fractional Helmholtz Equation

In this paper,we consider the Dirichlet problem of a 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,low-frequency asymptotic expansion and Runge approximation.We prove the global uniqueness of the three functions of the equation under low-frequency conditions.As the main result of this paper,it implies that one can use the external data to uniquely recover the unknown function of the equation in low-frequency case.However,these unique determination results are unknown in the local situation,hence the main result of this paper will be of important significance in photoacoustic tomography and thermoacoustic tomography.