Geodesic
Mathematical modeling of the equilibrium problem for a soft biological shell. I. Generalized statement
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 57-73
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A mathematical model of the equilibrium problem for a soft biological shell (small intestine) is constructed. The biological shell is modeled by a soft network shell formed by two families of mutually intersecting reinforcing filaments in the longitudinal and radial directions. A generalized formulation of the problem as a variational inequality with pseudomonotone operators is given. The solvability of the variational inequality is examined.
Keywords: soft biological shell, mathematical model, variational inequality, iterative method. 
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     title = {Mathematical modeling of the equilibrium problem for a~soft biological {shell.~I.} {Generalized} statement},
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G. R. Abdyusheva; I. B. Badriev; V. V. Banderov; O. A. Zadvornov; R. R. Tagirov. Mathematical modeling of the equilibrium problem for a soft biological shell. I. Generalized statement. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 57-73. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a5/

[1] Miftakhov R. N., “Chislennoe modelirovanie motoriki tonkoi kishki”, Sovremennye problemy biomekhaniki, 1989, no. 5, 147–183

[2] V. G. Alekseev, Yu. N. Afanasev, N. A. Yurina (red.), Gistologiya, Meditsina, M., 1983, 692 pp.

[3] Miftakhov R. N., “Prilozhenie teorii myagkikh obolochek v zadachakh biomekhaniki polykh organov”, Biomekhanika: problemy i issledovaniya, Zinatne, Riga, 1988, 57–64

[4] Ilgamov M. A., Miftakhov R. N., “Modelirovanie ritmicheskoi segmentatsii tonkoi kishki”, Meditsinskaya biomekhanika, Tr. Mezhdunar. konf., Riga, 1986, 164–177

[5] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972, 588 pp. | MR | Zbl

[6] Ridel V. V., Gulin B. V., Dinamika myagkikh obolochek, Nauka, M., 1990, 206 pp. | MR | Zbl

[7] Vainberg M. M., Variatsionnye metody issledovaniya nelineinykh operatorov, Gostekhizdat, M., 1956, 344 pp. | Zbl

[8] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978, 336 pp. | MR