On unique solvability of nonlocal drift–diffusion-type problems

We prove global existence and uniqueness of bounded weak solutions to Cauchy--Neumann problems for degenerate parabolic equations with drift terms determined by integral equations instead of by elliptic boundary problems as in the corresponding local case. Such problems arise as mathematical models of various transport processes driven by gradients of local particle concentrations and nonlocal interaction potentials. Examples are transport of charge carriers in semiconductors and phase separation processes in alloys