On a partial solution of the diffusion equation

Abstract

The process is considered of establishing the equilibrium spatial distribution of the concentration of particles in a one-dimensional bounded space region, subjected to a constant force normal to impermeable region boundaries. This process is described by the solution of the third boundary-value problem with homogeneous boundary conditions for the two-dimensional parabolic equation. It is shown that the found solution to the seemingly well-known problem of mathematical physics, but being of great importance in applications, cannot be obtained using theGreen’s function of this problem, known in the literature.