THE CONTROLLABILITY OF FOKKER--PLANCK EQUATIONS WITH REFLECTING BOUNDARY CONDITIONS AND CONTROLLERS IN DIFFUSION TERM.

One proves the exact controllability of the Fokker--Planck equation pt -- 1/2 Δ(up} -- div(bp) = 0,p(0) = ρ0,p(T) = p1,on aboundeddomain O with reflecting conditions on the boundary O. In particular, the exact controllability of stochastic differential equations with reflection to O is derived, and it is achieved by a nonlinear multivalued feedbac k controller u = Φ(., p), which steers p0 in p1 in a sufficiently large time T. [ABSTRACT FROM AUTHOR]