On the State Estimate for Two-Phases Stochastic Stefan Systems

Abstract

This paper is concerned with the state and free boundary estimates for two phases stochastic Stefan systems. The principal line of attack is to introduce the stochastic variational inequality as the system model, which plays a role to embed the free boundary condition into the basic system equation. Thus, the existence theorem of the solution is proved within the framework of Hilbert function space concept. Finally, both the state and free boundary estimator equations are derived by using the martingale and innovation approaches.