  The pointwise space-time behaviors of the Green's function and the global
solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in spatial three
dimension are studied in this paper. It is shown that the Green's function
consists of the diffusion waves decaying exponentially in time but
algebraically in space, and the singular kinetic waves which become smooth for
all $(t,x,v)$ when $t>0.$ Furthermore, we establish the pointwise space-time
behaviors of the global solution to the nonlinear VPFP system when the initial
data is not necessarily smooth in terms of the Green's function.

Analysis of PDEs