Geodesic
On one mathematical model of substance transfer in fractal media
Matematičeskoe modelirovanie, Tome 15 (2003) no. 9, pp. 17-28.

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Qualitatively new mathematical model of finite-size waves propagation in semi-boundless channel filled with liquid or gas and having flat parallel walls, which are surrounded by fractal media. For this model, which is a one-dimensional wave equation with fractional sum of $3/2$ order, existence of singular solution is proved. Co-structural form of this solution is established by Fourier method. Solution of Cauchy problem for this model is found by integral equations method for the case when the speed of filtration changes according to law which considers the effects of the filtration processes in fractal media. 
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     title = {On one mathematical model of substance transfer in fractal media},
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L. I. Serbina. On one mathematical model of substance transfer in fractal media. Matematičeskoe modelirovanie, Tome 15 (2003) no. 9, pp. 17-28. http://geodesic.mathdoc.fr/item/MM_2003_15_9_a1/

[1] Khlestkina N. M., Shagapov V. Sh., Prikladnaya matematika i tekhnicheskaya fizika, 37:5 (1996), 82–92 | Zbl

[2] Charnyi I. A., Neustanovivsheesya dvizhenie realnoi zhidkosti v trubakh, Nedra, M., 1975

[3] Polubarinova-Konina P. Ya., Teoriya dvizheniya gruntovykh vod, Nauka, M., 1977 | MR

[4] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995 | Zbl

[5] Nakhushev A. M., Elementy drobnogo ischisleniya i ikh primenenie, Izd-vo KBNTs RAN, Nalchik, 2000

[6] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966