ON WEAK SOLVABILITY OF MATHEMATICAL MODEL DESCRIBING THE MOTION OF POLYMER SOLUTIONS WITH MEMORY
- 作者: Zvyagin A.V1, Strukov M.I1
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隶属关系:
- Voronezh State University
- 期: 卷 60, 编号 10 (2024)
- 页面: 1422-1428
- 栏目: BRIEF MESSAGES
- URL: https://kld-journal.fedlab.ru/0374-0641/article/view/649606
- DOI: https://doi.org/10.31857/S0374064124100103
- EDN: https://elibrary.ru/JSZTMX
- ID: 649606
如何引用文章
详细
The weak solvability of the initial-boundary value problem describing the motion of weakly concentrated aqueous polymer solutions taking into account the memory of the fluid is considered in the paper. In this model the memory is considered along the trajectory of fluid particles, determined by the velocity field. The topological approximation approach and the theory of regular Lagrangian flows are used.
作者简介
A. Zvyagin
Voronezh State University
Email: zvyagin.a@mail.ru
Russia
M. Strukov
Voronezh State University
Email: mixail.strukov12@gmail.com
Russia
参考
- Voitkunskii, Y.I., Amfilokhiev, V.B., and Pavlovskii, V.A., Equations of motion of a fluid, with its relaxation properties taken into account, Trudy Leningrad. Korablestr. Inst., 1970, vol. 69, pp. 19–26.
- Pavlovskii, V.A., Theoretical description of weak aqueous polymer solutions, Dokl. Akad. Nauk SSSR, 1971, vol. 200, pp. 809–812.
- Pukhnachev, V.V. and Frolovskaya, O.A., On the Voitkunskii–Amfilokhiev–Pavlovskii model of motion of aqueous polymer solutions, Proc. Steklov Inst. Math., 2018, vol. 300, pp. 168–181.
- Frolovskaya, O.A. Analysis of the models of motion of aqueous solutions of polymers on the basis of their exact solutions / O.A. Frolovskaya, V.V. Pukhnachev // Polymer. — 2018. — V. 10. — P. 684.
- Zvyagin, A.V., Weak solvability of the nonlinearly viscous Pavlovskii model, Russ. Math., 2022, vol. 66, no. 6, pp. 73–78.
- Zvyagin, A.V., Optimal control problem for a stationary model of low concentrated aqueous polymer solutions, Differ. Equat., 2013, vol. 49, no. 2, pp. 246–250.
- Zvyagin, A.V., Study of solvability of a thermoviscoelastic model describing the motion of weakly concentrated water solutions of polymers, Siberian Math. J., 2018, vol. 59, no. 5, pp. 843–859.
- Zvyagin, A.V. Attractors for model of polymer solutions motion / A.V. Zvyagin // Discrete Contin. Dyn. Syst. — 2018. — V. 38, № 12. — P. 6305–6325.
- Zvyagin, A.V., Investigation of the weak solubility of the fractional Voigt alpha-model, Izv. Math., 2021, vol. 85, no. 1, pp. 61–91.
- Zvyagin, A.V. and Kostenko, E.I., On the existence of feedback control for one fractional Voigt model, Differ. Equat., 2023, vol. 59, no. 12, pp. 1778–1783.
- Rivlin, R.S. Stress deformation relations for isotropic materials / R.S. Rivlin, J.L. Ericksen // Arch. Rational Mech. Anal. — 1955. — V. 4. — P. 323–425.
- Fursikov, A.V., Optimal Control of Distributed Systems. Theory and Applications, Providence: Amer. Math. Soc., 2000.
- Zvyagin, V.G. and Turbin, M.V., Matematicheskiye voprosy gidrodinamiki vyazkouprugikh sred (Mathematical Questions in the Hydrodynamics of Viscoelastic Media), Moscow: KRASAND URSS, 2012.
- Orlov, V.P. On mathematical models of a viscoelasticity with a memory/ V.P. Orlov, P.E. Sobolevskii // Differ. Integral Equat. — 1991. — V. 4. — P. 103–115.
- Zvyagin, V.G. and Dmitrienko, V.T., On weak solutions of a regularized model of a viscoelastic fluid, Differ. Equat., 2002, vol. 38, no. 12, pp. 1731–1744.
- DiPerna, R.J. Ordinary differential equations, transport theory and Sobolev spaces / R.J. DiPerna, P.L. Lions // Invent. Math. — 1989. — V. 98, № 3. — P. 511–547.
- Crippa, G. Estimates and regularity results for the diPerna–Lions flow / G. Crippa, C. de Lellis // J. Reine Angew. Math. — 2008. — V. 616. — P. 15–46.
- Crippa, G. The ordinary differential equation with non-Lipschitz vector fields / G. Crippa // Boll. Unione Mat. Ital. — 2008. — V. 1, № 2. — P. 333–348.
- Sadovskii, B.N., Limit-compact and condensing operators, Russ. Math. Surv., 1972, vol. 27, no. 1, pp. 85–155.
- Dmitrienko, V.T. and Zvyagin, V.G., Homotopy classification of a class of continuous mappings, Math. Notes, 1982, vol. 31, no. 5, pp. 404–410.
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