Nonlocal model of diffusion-advection radon in ground-atmosphere
Matematičeskoe modelirovanie, Tome 22 (2010) no. 9, pp. 95-106.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper analytical solutions in terms of the generalized Wright function for a nonlocal model of advection-diffusion of radon in the soil atmosphere are obtained. It is shown that the solutions for specific values of the fractal characteristics transform in the previously known classical solutions.
Mots-clés : radon, diffusion, advection.
Keywords: fractal environment, soil-atmosphere system
@article{MM_2010_22_9_a6,
     author = {R. I. Parovik},
     title = {Nonlocal model of diffusion-advection radon in ground-atmosphere},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {22},
     number = {9},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_9_a6/}
}
TY  - JOUR
AU  - R. I. Parovik
TI  - Nonlocal model of diffusion-advection radon in ground-atmosphere
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 95
EP  - 106
VL  - 22
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_9_a6/
LA  - ru
ID  - MM_2010_22_9_a6
ER  - 
%0 Journal Article
%A R. I. Parovik
%T Nonlocal model of diffusion-advection radon in ground-atmosphere
%J Matematičeskoe modelirovanie
%D 2010
%P 95-106
%V 22
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2010_22_9_a6/
%G ru
%F MM_2010_22_9_a6
R. I. Parovik. Nonlocal model of diffusion-advection radon in ground-atmosphere. Matematičeskoe modelirovanie, Tome 22 (2010) no. 9, pp. 95-106. http://geodesic.mathdoc.fr/item/MM_2010_22_9_a6/

[1] Novikov G. F., Kapkov Yu. N., Radioaktivnye metody razvedki, Nedra, L., 1965, 759 pp.

[2] Rudakov V. P., “Monitoring napryazhenno-deformirovannogo sostoyaniya porod seismoaktivnogo regiona emanatsionnym metodom”, Geokhimiya, 1986, no. 9, 1337–1342

[3] Firstov P. P., “Monitoring ob'emnoi aktivnosti podpochvennogo radona $^{222}\text{Rn}$ na paratunskoi geotermalnoi sisteme v 1997–1998 gg. s tselyu poiska predvestnikov silnykh zemletryasenii Kamchatki”, Vulkanologiya i seismologiya, 1999, no. 6, 33–43

[4] Firstov P. P., Rudakov V. P., “Rezultaty registratsii podpochvennogo radona v 1997–2000 gg. na Petropavlovsk-Kamchatskom geodinamicheskom poligone”, Vulkanologiya i seismologiya, 2002, no. 6, 1–16

[5] Kupovykh G. V., Morozov V. N., Shvarts Ya. M., Teoriya elektrodnogo effekta v atmosfere, TRGU, Taganrog, 1998, 122 pp.

[6] Meilanov R. P., Magomedov R. M., Shabanova M. R., Akhmedova G. M., “Zadacha bez nachalnykh uslovii dlya nelokalnogo uravneniya teploprovodnosti”, Materialy Mezhdunarodnogo Rossiisko-Abkhazskogo simpoziuma “Uravneniya smeshannogo tipa i rodstvennye problemy analiza i informatiki” i VII Shkoly molodykh uchenykh “Nelokalnye kraevye zadachi i problemy sovremennogo analiza i informatiki” (Nalchik-Elbrus, 17–22 maya 2009 g.), KBNTs RAN, Nalchik, 2009, 162–165

[7] Bedanokova S. Yu., Matematicheskoe modelirovanie vodnogo i solevogo rezhimov v pochvakh s fraktalnoi organizatsiei, Avtoref. Dissertatsii kand. fiz.-mat. nauk, Taganrog, 2007, 16 pp.

[8] Serbina L. I., Nelokalnye matematicheskie modeli perenosa v vodonosnykh sistemakh, Nauka, M., 2006, 167 pp.

[9] Metzler R., Klafter J., “The random walk`s guide to anomalous diffusion: a fractional dynamics approach”, Physics Reports, 339 (2000), 1–77 | DOI | MR | Zbl

[10] Parovik R. I., Shevtsov B. M., Firstov P. P., “Model perenosa radona (222Rn) v rezhime superdiffuzii vo fraktalnoi srede”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 10:1 (2008), 79–85 | MR

[11] Parovik R. I., Shevtsov B. M., “Modelirovanie protsessov perenosa radona v sredakh s fraktalnoi strukturoi”, Matematicheskoe modelirovanie, 21:8 (2009), 30–36 | Zbl

[12] Grammakov A. G., Nikonov A. I., Tarfeev G. P., Radiometricheskie metody poiskov i razvedki uranovykh rud, Gosgeoltekhizdat, M., 1957, 610 pp.

[13] Bulashevich Yu. P., Khairetdinov R. K., “K teorii diffuzii emanatsii v poristykh sredakh”, Izvestiya AN SSSR. Seriya geofizicheskaya, 1959, no. 12, 1787–1792

[14] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp. | Zbl

[15] Ozturk I., “On the Theory of Fractional Equation”, Reports of Adyghe (Circassian) International Academy of Sciences, 3:2 (1998), 35–39

[16] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966, 672 pp. | Zbl

[17] Kilbas A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006, 523 pp. | MR | Zbl

[18] Prudnikov A. P., Brychkov Yu. A., Marychev I. O., Integraly i ryady. Spetsialnye funktsii. Dopolnitelnye glavy, Fizmatlit, M., 2003, 688 pp. | MR

[19] The wolfram functions site, [Elektronnyi resurs], Wolfram Research, Inc., 1998, svobodnyi, zagl. s ekrana Rezhim dostupa: http://functions.wolfram.com

[20] Prudnikov A. P., Brychkov Yu. A., Marychev I. O., Integraly i ryady. Spetsialnye funktsii, v. 2, Nauka, M., 1983, 752 pp. | MR | Zbl

[21] Spivak A. A., Sukhorukov M. V., Kharlamov V. A., “Osobennosti emanatsii radona ($^{222}\text{Rn}$) s glubinoi”, Doklady RAN, 420:2 (2008), 825–828