An inverse source problem for nonlocal Fokker-Planck equations involving nonlinear force fields

Abstract

We study a source identification problem for a class of nonlocal Fokker-Planck equations, where the force field depends on the state function. Our aim is to find some suitable conditions ensuring the solvability of the problem and the Hölder regularity of solutions. The main ingredient of our analysis is the regularity estimates, established for resolvent operators in Hilbert scales, that allow us to employ the fixed point argument. Some specific cases of kernel function are discussed.