Study of heat equations with boundary differential equations

Abstract

Solutions of heat or diffusion equations with the boundary conditions which is a dynamic random field are discussed. This kind of method can be used to obtain the description of heat equations or diffusion equations based on observed physical reality, ie ordinary differential equations, representing heat or diffusion propagation, with a boundary condition that satisfies stochastic differential equations. The heat or diffusion equations obtained from the method are the compared to the heat equation or the stochastic diffusion. The comparison is emphasized on the existence and properties of Green functions.