The Mathematical Modelling of Diffusion and Advection of Radon in Piecewise Anisotropic Layered Media with Inclusions

The use of radon in various areas of science and technology keeps growing. In the radiation safety aspect, the interest to radon stems from the need to protect people from the pathogenic impact of ionization produced by this element and its decay products. The other part of the problem of radon has to do with the fact that radon is an indicator of seismogeodynamic activity in the continental crust. Its study can contribute substantially to the understanding of fault tectonics and yield significant information for seismic forecasts. Some insufficiently studied questions remain related to identifying and describing the processes and mechanics of radon transfer in various media, the factors shaping the temporal and spatial dynamics of the radon field, which is of interest for locating hydrocarbon deposits. All that together promotes the active development of methods for modelling mathematically the transfer of radon and its decay products in various media, including anisotropic media.
In this article we construct a mathematical model of radon diffusion in layered anisotropic media with anisotropic inclusions, which amounts to a parabolic-type boundary value problem of mathematical physics. We propose a combined method for solving the problem based on integral transformations, integral representations, and boundary integral equations.

Keywords

diffusion-advection of radon; anisotropic media; boundary problem; method of integral transformations and integral representations; Laplace transform.

References

1. Utkin V.I. [Gas Breath of Earth]. Sorosovskiy obrazovatel'nyy zhurnal, 1997, no. 1, pp. 57-64. (in Russian)
2. Yakovleva V.S., Parovik R.I. [The Numerical Solution of the Advection-Diffusion Equation of Radon in Multilayered Geological Media]. Vestnik KRAUNTs. Fiz.-mat. nauki, 2011, no. 1 (2), pp. 45-55. (in Russian)
3. Krizskiy V.N. [About a Way of Calculation of Physical Fields in Piecewise and Anisotropic Media. Part II. Non-stationary Fields]. Vestnik Bashkirskogo universiteta, 2009, vol. 14, no. 4, pp. 1302-1306. (in Russian)
4. Matveeva T.A. Nekotorye metody obrashcheniya preobrazovaniya Laplasa i ikh prilozheniya: dis ... kand. fiz.-mat. nauk [Laplace Transform Some Methods of the Inversion of the Laplace Transform and Their Applications: Dissertation of the Candidate of Physical and Mathematical Sciences]. Sankt-Peterburg, 2003.