On a Moving Boundary Solution to the Fokker-Planck Equation for Particle Transport in Turbulent Flows with Absorbing Boundaries

A Fokker—Planck equation describing the transport of particlesin turbulent flows is considered. The initial value problemwith perfectly absorbing boundary conditions on the wall issolved by introducing a characteristic line in phase space.It is found that the solution domain in phase space decomposesinto three regions which are connected by two moving boundaries,and the moving boundaries can be found explicitly. For Gaussian-typeinitial conditions, the solution of the Fokker—Planckequation can be obtained in each of the three regions by solvinga diffusion equation. An approximation procedure for the generalinitial value problem is established and the approximate solutionsequence is shown to be convergent in a certain Hilbert space.