The use of the heat operator in an existence theory problem of the Vlasov equation

Abstract

A use is demonstrated for aparabolic operator in the context of the context of the existence theory problem of te Vlasov-Poisson system. It is shown that some aspects of the evolution of the field can be viewed as a diffusion porcess and that relevant estimates on the field can be derived through the use of the heat operator. The application of this to the existence theory problem is demonstrated.