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Diffusion Path in Ternary One-Phase Systems: An Overview

Serafin D., Nowak W. J., Wierzba P., Wędrychowicz S., Wierzba Bartek

Advances in Manufacturing Science and Technology

2020

Vol. 44, nr 1

1--8

In this article, the fundamental questions concerning the diffusion path, in particular, what is the shape of diffusion path in ternary systems and how to approximate it from the initial concentration profile, will be answered. The new rules were found which allow for determining the diffusion path from a known initial concentration of the components. This approximation will allow for designing new materials without a time-consuming numerical simulation of the full system of equations. It is shown that the difference in intrinsic diffusion coefficients determines the up-hill diffusion.

On solutions of stochastic integral equations

Malczak J., Wędrychowicz S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

[Z] 42(1)

75-85

We deal with the stochastic integral equation [formula]. Sufficient conditions for the existence and uniqueness of random solution and its asymptotic behaviour are given. We use the Banach space of tempered functions which contains the space D(([0,+ ])and we apply the Banach fixed point principle.