ON A 3D INITIAL-BOUNDARY VALUE PROBLEM FOR DETERMINING THE DYNAMICS OF IMPURITIES CONCENTRATION IN A HORIZONTAL LAYERED FINE-PORE MEDIUM

Sharif E. Guseynov, Ruslans Aleksejevs, Jekaterina V. Aleksejeva


Last modified: 14.05.2019

Abstract

In the present paper, we propose an analytical approach for solving the 3D unsteady-state boundary-value problem for the second-order parabolic equation with the second and third types boundary conditions in two-layer rectangular parallelepipedic domain.

Keywords


unsteady-state diffusion equation; initial-boundary value problem; Robin boundary condition; analytical method

References


[1]     E. Teirumnieka, I. Kangro, E. Teirumnieks, and H. Kalis, "The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers," The 10th International Scientific and Practical Conference "Environment. Technology. Resources", vol. III, June 18-20, 2015, Rezekne, Latvia, pp. 186-192. |Online|. Available: http://journals.ru.lv/index.php/ETR/article/view/618/714. |Accessed: March 15, 2017.

[2]     I. Kangro, H. Kalis, A. Gedroics, E. Teirumnieka, and E. Teirumnieks, "On mathematical modelling of metals distributions in peat layers," Journal of Mathematical Modelling and Analysis, vol. 19, no. 4, pp. 568-588, 2014.

[3]     E. Teirumnieka, E. Teirumnieks, I. Kangro, H. Kalis, and A. Gedroics, "The mathematical modelling of Ca and Fe distribution in peat layers," The 8th International Scientific and Practical Conference "Environment. Technology. Resources", vol. II, June 20-22, 2011, Rezekne, Latvia, pp. 40-47, 2011.

[4]     H. Orru and M. Orru, "Sources and distribution of trace elements in Estonian peat," Journal of Global and Planetary Change, vol. 53, no. 4, pp. 249-258, 2006.

[5]     P. A. Brown, S. A. Gill, and S. J. Allen, "Metal removal from wastewater using peat," Journal of Water Research, vol. 34, no. 16, pp. 3907-3916, 2000.

[6]     A. N. Tikhonov and A. A. Samarsky, Equations of Mathematical Physics. New York: Dover Publications, 1990, xvi+765 p.

[7]     A. N. Tikhonov and V. Ya. Arsenin, Solution of Ill-posed Problems. Washington: Winston & Sons, 1977, xiii+258 p.

[8]     S. A. Andreyev and Sh. E. Guseynov, Regularizing algorithms for diagnosing: Applied to gas turbine engines in operation. Monograph. Saarbrücken: LAP Publishing, 2013, 116 p.

[9]     M. A. Al-Gwaiz, Sturm-Liouville Theory and its Applications. London: Springer-Verlag, 2008, x+264 p.

[10]   B. M. Levitan and I. S. Sargsyan, Sturm-Liouville and Dirac Operators. Dordrecht: Kluwer Academic Publications, 1991, xi+350 p.

[11]   V. A. Steklov, Fundamental Problems of Mathematical Physics. Moscow: Science, 1983, 432 p.

[12]   V. A. Il'in and E. G. Poznyak, Fundamentals of Mathematical Analysis, Part II. Moscow: Science, 1980, 448 p.

[13]   A. A. Abrikosov, L. P. Gor'kov, and I. E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics. Englewood Cliffs: Prentice-Hall, 1963, xv+352 p.

[14]   L. S. Levitov and A. V. Shitov, Green's Functions: Problems with Solutions. Moscow: FizMatLit, 2002, 252 p.

[15]   V. M. Babich, V. B. Kapilevich, S. G. Mikhlin, G. I. Natanson, P. M. Riz, L. N. Slobodetsky, and M. M. Smirnov, Linear Equation of Mathematical Physics. Moscow: Science, 1964, 368 p.

 






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