Variational Procedure of Deriving Diffusion Equation for Spreading in Porous Media

DOI: 10.4236/am.2013.410191   PDF   HTML   XML   3,141 Downloads   4,243 Views  

Abstract

We proposed the mathematical model and concrete example of how to use the notion of functional derivatives in order to arrive at a macroscopic equation for dispersion in disordered media. In the sake of simplicity, we considered the case of random process being a Gaussian process.

Share and Cite:

Logvinova, K. (2013) Variational Procedure of Deriving Diffusion Equation for Spreading in Porous Media. Applied Mathematics, 4, 1412-1416. doi: 10.4236/am.2013.410191.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] K. Logvinova and O. Kozyrev, “Models for the Average of the Solutions to a P.D.E. with Stochastic Coefficients,” European Journal of Scientific Research, Vol. 45, No. 3, 2010, pp. 383-390.
[2] O. Kozyrev and K. Logvinova, “Small Scale Models for the Spreading of Matter in Disordered Porous Media,” European Journal of Scientific Research, Vol. 45, No. 1, 2010, pp. 64-78.
[3] O. Kozyrev, “Diffusion Fractional Models for a Complex Porous Media in a Random Force Field for 3D Case,” European Journal of Scientific Research, Vol. 95, No. 3, 2013, pp. 436-443.
[4] V. I. Klyatskin “Waves and Stochastic Equations in Randomly Inhomogeneous Media,” Edition de Physique, Paris, 1985.
[5] K. Logvinova and M.-C. Neel, “A Fractional Equation for Anomalous Diffusion in a Randomly Heterogeneous Po rous Media,” Chaos, Vol. 14, No. 4, 2004, pp. 982-987. http://dx.doi.org/10.1063/
1.1796211
[6] E.A. Novikov, “Functionals and Random Force Methods for Turbulence Theory,” Journal of Experimental and Theoretical Physics, Vol. 47, No. 5, 1964, p. 1919.
[7] M. Donsker, “On Function Space Integrals,” Proceedings of a Conference on the Theory and Applications of Analysis in Function Space, M.II. Press, Cambridge, 1964, pp. 17-30.
[8] K. Furutsu, “On the Statistical Theory of Electromagnetic Waves in a Fluctuating Medium,” Journal of Research of the National Bureau of Standards, Vol. 67D, No. 3, 1963, p. 303.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.