Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 06, pp. 1-20.

Title: The Vlasov equation with strong magnetic field and oscillating
       electric field as a model for isotop resonant separation
   
Authors: Emmanuel Frenod (Univ. de Bretagne Sud, Vannes, France)
         Frederique Watbled (Univ. Rennes 1,  Beaulieu, France)

Abstract:  
  We study the qualitative behavior of solutions to the Vlasov equation
  with strong external magnetic field and oscillating electric
  field. This model is relevant to the understanding of isotop
  resonant separation.  We show that the effective equation is
  a kinetic equation with a memory term.  This memory term involves
  a pseudo-differential operator whose kernel is characterized by an
  integral equation involving Bessel functions. The kernel is explicitly
  given in some particular cases.

Submitted November 24, 2001. Published January 10, 2002.
Math Subject Classifications: 82D10, 35B27, 35Q99, 76X05, 47G10, 47G20.
Key Words: Vlasov equation; Homogenization; Two-scale convergence;
    Memory effects; Pseudo-differential equations; Isotop separation.