Numerical solution of an integrodifferential equation of heat conduction for~nonlocal medium
Matematičeskoe modelirovanie, Tome 25 (2013) no. 5, pp. 99-108.

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The mathematical model of heat conduction in nonlocal medium with internal friction is proposed on the basis of the relations of rational thermodynamics of irreversible processes. One-dimensional numerical solution of an integrodifferential equation of heat conduction was obtained by the finite elements method.
Keywords: nonlocal medium, internal state parameters, integrodifferential equation of heat conduction, finite elements method.
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G. N. Kuvyrkin; I. Y. Savelyeva. Numerical solution of an integrodifferential equation of heat conduction for~nonlocal medium. Matematičeskoe modelirovanie, Tome 25 (2013) no. 5, pp. 99-108. http://geodesic.mathdoc.fr/item/MM_2013_25_5_a7/

[1] Gusev A. I., Nanomaterialy, nanostruktury, nanotekhnologii, Fizmatlit, M., 2005, 410 pp.

[2] Andrievskii R. A., Ragulya A. V., Nanostrukturnye materialy, Izd. tsentr “Akademiya”, M., 2005, 192 pp.

[3] Kobayasi N., Vvedenie v nanotekhnologiyu, Per. s yaponsk., BINOM. Laboratoriya znanii, M., 2005, 134 pp.

[4] Pul-ml. Ch., Ouenc F., Nanotekhnologii, Tekhnosfera, M., 2006, 336 pp.

[5] Mileiko S. T., “Kompozity i nanostruktury”, Kompozity i nanostruktury, 2009, no. 1, 6–37 | MR

[6] Kuvyrkin G. N., Termomekhanika deformiruemogo tverdogo tela pri vysokointensivnom nagruzhenii, Izd. MGTU, M., 1993, 142 pp.

[7] Zarubin B. C., Kuvyrkin G. N., “Matematicheskaya model relaksiruyuschego tverdogo tela pri nestatsionarnom nagruzhenii”, Dokl. RAN, 345:2 (1995), 193–195 | Zbl

[8] Zarubin B. C., Kuvyrkin G. N., “Matematicheskoe modelirovanie termomekhanicheskikh protsessov pri intensivnom teplovom vozdeistvii”, Teplofizika vysokikh temperatur, 41:2 (2003), 300–309

[9] Zarubin B. C., Kuvyrkin G. N., Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoi sredy, Izd. MGTU im. N. E. Baumana, M., 2008, 512 pp.

[10] Onami M. i dr., Vvedenie v mikromekhaniku, Per. s yaponsk., Metallurgiya, M., 1987, 280 pp.

[11] Krivtsov A. M., Deformirovanie i razrushenie tverdykh tel s mikrostrukturoi, Fizmatlit, M., 2007, 304 pp.

[12] Eringen A. Cemal, Nonlocal continuum field theories, Springer-Verlag, New York, 2002, 376 pp. | MR

[13] Zarubin V. S., Kuvyrkin G. N., Saveleva I. Yu., “Nelokalnaya matematicheskaya model teploprovodnosti v tverdykh telakh”, Vestnik MGTU im. N. E. Baumana, ser. Estestv. Nauki, 2011, no. 3, 20–30

[14] Troschiev V. E., Shagaliev R. M., “Konservativnye uzlovye skhemy metodov konechnykh raznostei i konechnykh elementov dlya dvumernogo uravneniya teploprovodnosti”, Chislennye metody mekhaniki sploshnoi sredy, 15:4 (1984), 131–157

[15] Akin J. E., Application and implementation of finite element method, Acad. Press, London, 1982, 372 pp. | MR | Zbl