R.I.354

SOME REMARKS ON MEASURE SOLUTIONS OF THE VLASOV EQUATION

B.Bodin
Centre d'Etudes de Limeil-Valenton, 
94195 Villeneuve-Saint-Georges Cedex, France

P.A.Raviart
Centre de Math\'ematiques Appliqu\'ees, Ecole Polytechnique, 
F. 91128 Palaiseau Cedex, France


Abstract.
 The mathematical modeling of electron or ion beams leads to 
consider boundary value problems for the stationary Vlasov equation where the 
boundary data are measures and moreover the data depend on a parameter. 
We give in this paper natural sufficient conditions for such a boundary
 problem 
to be well posed and we derive an explicit form of the corresponding measure 
solution and of its derivative with respect to the parameter.

 Key-words.
Convection equations, Vlasov equation, measure solutions.


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