Theoretical analysis and numerical implementation of a stationary diffusion–drift model of polar dielectric charging

The global solvability and local uniqueness of the solution of a boundary value problem for the model of electron-induced charging of polar dielectrics are proved. The model is described by a semilinear diffusion–drift equation and Maxwell's equations, which relate the charge density and the electric field. For the charge density function, the maximum and minimum principle is established, which is used to control the data of the computational experiment. The results of a finite element implementation of a mathematical model of polar dielectric charging under conditions of electron irradiation are presented and discussed.