Computational experiments for one class of mathematical models in thermodynamics and hydrodynamics
Journal of computational and engineering mathematics, Tome 4 (2017) no. 1, pp. 16-26.

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The article contains the results of computational experiments for the Dzeczer mathematical model and the generalized Fisher – Kolmogorov mathematical model. Information on the solvability of the studied models is given. We describe both an algorithm to find an approximate solution of mathematical models of thermodynamics and hydrodynamics, and implementation of the algorithm as a program in the computer mathematics system Maple. The results of computational experiments for the studied models are presented.
Keywords: evolution equation, Dzektser mathematical model, generalized Fisher – Kolmogorov mathematical model, numerical solution, projection method.
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J. K. T. Al-Isawi. Computational experiments for one class of mathematical models in thermodynamics and hydrodynamics. Journal of computational and engineering mathematics, Tome 4 (2017) no. 1, pp. 16-26. http://geodesic.mathdoc.fr/item/JCEM_2017_4_1_a1/

[1] P. Ya. Polubarinova-Kochina, Teoriya dvizheniya gruntovykh vod, Nauka, M., 1977, 664 pp. | MR

[2] E. S. Dzektser, “Obobschenie uravneniya dvizheniya gruntovykh vod so svobodnoi poverkhnostyu”, DAN SSSR, 202:5 (1972), 1031–1033 | Zbl

[3] G. A. Sviridyuk, S. A. Zagrebina, “Neklassicheskie modeli matematicheskoi fiziki”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 7–18 | Zbl

[4] M. C. Cross, P. C. Hohenberg, “Pattern formation outside of equilibrium”, Reviews of Modern Physics, 65 (1993), 851–1112 | DOI

[5] G. T. Dee, W. van Saarloos, “Bistable systems with propagating fronts leading to pattern formation”, Physical Review Letters, 60 (1988), 2641–2644 | DOI

[6] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, v. 42, Inverse and Ill-Posed Problems Series, de Gruyer, 2012, 216+viii pp. | DOI | MR

[7] G. A. Sviridyuk, “Phase portraits of Sobolev-type semilinear equations with a relatively strongly sectorial operator”, St. Petersburg Math. J., 6:5 (1995), 1109–1126 | MR | Zbl

[8] A. Favini, A. Yagi, Degenerate differential equation in Banach spaces , Marcel Dekker Inc., N.-Y.; Basel; Hong Kong, 1999, 312 pp. | MR

[9] G. A. Sviridyuk, S. V. Brychev, “Numerical solution of systems of equations of Leontief type”, Russian Math. (Iz. VUZ), 47:8 (2003), 44–50 | MR | Zbl

[10] J. K. T. Al-Isawi, A. A. Zamyshlyaeva, “Computational experiment for one class of evolution mathematical models in quasi-Sobolev spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:4 (2016), 141–147 | DOI

[11] A. A. Zamyshlyaeva, D. K. T. Al-Isawi, “On some properties of solutions to one class of evolution Sobolev type mathematical models in quasi-Sobolev spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:4 (2015), 113–119 | DOI | Zbl

[12] A. V. Keller, Issledovanie ogranichennykh reshenii lineinykh uravnenii tipa Soboleva, diss. ...kand. fiz.-matem. nauk, Chelyabinsk, 1997, 115 pp.