화학공학소재연구정보센터
SIAM Journal on Control and Optimization, Vol.59, No.1, 709-726, 2021
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 rho(t) - 1/2 Delta(u rho) - div(b rho) = 0, rho(0) = rho(0), rho(T) = rho(1), on a bounded domain O with reflecting conditions on the boundary partial derivative O. In particular, the exact controllability of stochastic differential equations with reflection to partial derivative O is derived, and it is achieved by a nonlinear multivalued feedback controller u = Phi(., rho), which steers rho(0) in rho(1) in a sufficiently large time T.