On the propagation of the bulk of a mass subject to periodic convection and diffusion
exist, and u —> 0 and du/dx —> 0 as \x\ —+ oo (at rates sufficiently rapid to justify certain integrations by parts). Here u(x, t) is the density, and f(x) is the initial density, of a mass distribution that is convected with velocity a(x) (the drift coefficient) and is subject to diffusion, the positive coefficient b(x) being the diffusion coefficient. Our purpose is to study the manner in which the bulk of the mass is dispersed. The well posedness of the problem is ensured by the standard theory of Co-semigroups, which also guarantees that the positivity of the initial density is preserved [1]. Equation (1) arises in many scientific and technical applications; a recent review of the Fokker-Planck equation has been given by Miyazawa [2], where the relationship of this equation with the Schroedinger equation is discussed and an entire section is