Abstract
The purpose of this paper is to formulate the stochastic electron beam processing systems. First, the mathematical model of the stochastic electron beam processing system is given. It is shown that the electron beam system leads us to the so-called free boundary problems of the Stefan type. Secondly, by using the change of variables and introducing the appropriate function spaces, the stochastic electron beam processing systems is transformed to the stochastic variational inequality. Finally, the existence and uniqueness properties of the solution of the stochastic variational inequality are proved by using the method of Galerkin.
