ON A MATHEMATICAL MODEL DESCRIBING THE MOTION OF SOLID PARTICLES OF MICRO- AND NANO-SIZE IN GAS FLOW
In the present article, a mathematical model is developed to describe the motion of solid particles of micro- and nano-size in a gaseous medium. The model is represented by certain integro-differential equation with appropriate initial and boundary conditions. A probabilistic interpretation of the model is provided and its solvability is studied. We find that unique solution exists at certain sufficient condition. It is shown that the Fokker-Planck equation can be obtained from the integro-differential equation. Finally, a generalization to the 2D case is performed.