GLOBAL WEAK SOLUTIONS FOR THE INITIAL-BOUNDARY-VALUE PROBLEMS TO THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

This work is devoted to prove the existence of weak solutions of the k inetic Vlasov-Poisson-Fokker-Planck system in bounded domains for attr active or repulsive forces. Absorbing and reflection type boundary con ditions are considered for the kinetic equation and zero values for th e potential on the boundary. The existence of weak solutions is proved for bounded and integrable initial and boundary data with finite ener gy. The main difficulty of this problem is to obtain an existence theo ry for the linear equation. This fact is analysed using a variational technique and the theory of elliptic-parabolic equations of second ord er. The proof of existence for the initial-boundary value problems is carried out following a procedure of regularization and linearization of the problem. (C) 1998 B. G. Teubner Sturtgart-John Wiley & Sons, Lt d.