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2. Aristov, S.N. and Skulskii, O.I. Exact solution of the problem on a six‐constant Jeffreys model of fluid in a plane channel. Journal of Applied Mechanics and Technical Physics, 2002, 43, 817–822. DOI: 10.1023/A:1020752101539.
3. Aristov, S.N. and Skulskiy, O.I. Viscoelastic effects of blood flow in nondeformable. Russian Journal of Biomechanics, 1999, 3 (4), 24–33.
4. Chhabra, R.P. and Richardson, J.F. Non‐Newtonian Flow in the Process Industries: Fundamentals and Engineering Applications, 1st ed., Butterworth‐Heinemann, Oxford, UK, 1999, 436 p.
5. Middleman, S. Fundamentals of Polymer Processing, McGraw-Hill, 1977, 525 p.
6. Bird, R.B., Armstrong, R.C., and Hassager, O. Dynamics of Polymeric Liquids, vol. 1: Fluid Mechanics, 2nd ed., Wiley, 1987, 672 p.
7. Tanner, R.I. Engineering Rheology, 2nd ed., OUP Oxford, 2000, 586 p.
8. Schowalter, W.R. Mechanics of Non-Newtonian Fluids, Pergamon Press, 1978, 300 p.
9. Hartnett, J.P. and Kostic, M. Heat transfer to a viscoelastic fluid in laminar flow through a rectangular channel. International Journal of Heat and Mass Transfer, 1985, 28 (6), 1147–1155. DOI: 10.1016/0017-9310(85)90122-X.
10. Aristov, S.N. and Keller, I.E. Beltrami stress fields in an elastic body. Doklady Physics, 2016, 61 (7), 343–346. DOI: 10.1134/S1028335816070065.
11. Gubareva, K.V. and Prosviryakov, E.Yu. Exact analytical solution to the problem of stationary convection in the Boussinesq approximation with account for viscous dissipation. Diagnostics, Resource and Mechanics of materials and structures, 2025, 6, 23–38. DOI: 10.17804/2410-9908.2025.6.023-038. Available at: http://dream-journal.org/issues/2025-6/2025-6_528.html
12. Ershkov, S.V., Prosviryakov, E.Yu, Burmasheva, N.V., and Christianto, V. Towards understanding the algorithms for solving the Navier-Stokes equations. Fluid Dynamics Research, 2021, 53 (4), 044501. DOI: 10.1088/1873-7005/ac10f0.
13. Ershkov, S., Burmasheva, N., Leshchenko, D.D., and Prosviryakov, E.Yu. Exact solutions of the Oberbeck-Boussinesq equations for the description of shear thermal diffusion of Newtonian fluid flows. Symmetry, 2023, 15 (9), 1730. DOI: 10.3390/sym15091730.
14. Ershkov, S.V., Prosviryakov, E.Yu., Burmasheva, N.V., and Christianto, V. Solving the hydrodynamical system of equations of inhomogeneous fluid flows with thermal diffusion: a review. Symmetry 2023, 15, 1825. DOI: 10.3390/sym15101825.
15. Gubareva, K.V., Prosviryakov, E.Yu., and Eremin, A.V. An exact solution with inhomogeneous boundary conditions for a steady non-uniform Couette flow between permeable plates. Diagnostics, Resource and Mechanics of materials and structures, 2025, 5, 66–86. DOI: 10.17804/2410-9908.2025.5.066-086. Available at: http://dream-journal.org/issues/2025-5/2025-5_522.html
16. Chang, H.-C. and Demekhin, E.A. Studies in Interface Science, vol. 14: Complex Wave Dynamics on Thin Films, Elsevier, 2002, 412 p.
17. Kalliadasis, S., Ruyer-Quil, C., Scheid, B., and Velarde, M.G. Falling Liquid Films, series Applied Mathematical Sciences, Springer, London, 2012. DOI: 10.1007/978-1-84882-367-9.
18. Baranovskii, E.S. Prosviryakov, E.Yu., and Ershkov, S.V. Mathematical analysis of steady non-isothermal flows of a micropolar fluid. Nonlinear Analysis: Real World Applications, 2025, 84, 104294. DOI: 10.1016/j.nonrwa.2024.104294.
19. Ershkov, S.V., Baranovskii, E.S., Prosviryakov, E.Yu., and Yudin, A.V. Non-Newtonian rivulet-flows on unsteady heated plane surface. International Journal of Non-Linear Mechanics, 2025, 170, 104984. DOI: 10.1016/j.ijnonlinmec.2024.104984.
20. Gubareva, K.V., Prosviryakov, E.Yu., and Eremin, A.V. Inhomogeneous Couette–Poiseuille flow of a viscous incompressible fluid in an infinite horizontal layer with permeable boundaries. Diagnostics, Resource and Mechanics of Materials and Structures, 2025, 5, 6–28. DOI: 10.17804/2410-9908.2025.5.006-028. Available at: http://dream-journal.org/issues/2025-5/2025-5_523.html
21. Baranovskii, E.S. Analytical Solutions to the unsteady Poiseuille flow of a second grade fluid with slip boundary conditions. Polymers, 2024, 16 (2), 179. DOI: 10.3390/polym16020179.
22. Denier, J.P. and Dabrowski, P.P. On the boundary-layer equations for power-law fluids. In: Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 2004, 460, 3143–3158. DOI: 10.1098/rspa.2004.1349.
23. Frigaard, I.A. and Ryan, D.P. Flow of a visco-plastic fluid in a channel of slowly varying width. Journal of Non-Newtonian Fluid Mechanics, 2004, 123 (1), 67–83. DOI: 10.1016/j.jnnfm.2004.06.011.
24. Málek, J., Rajagopal, K.R., and Růžička, M. Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity. Mathematical Models and Methods in Applied Sciences, 1995, 05 (06), 789–812. DOI: 10.1142/S0218202595000449.
25. Massoudi, M. and Phuoc, T.X. Fully developed flow of a modified second grade fluid with temperature dependent viscosity. Acta Mechanica, 2001, 150, 23–37. DOI: 10.1007/BF01178542.
26. Mekheimer, Kh.S. and El Kot, M.A. The micropolar fluid model for blood flow through a tapered artery with a stenosis. Acta Mechanica Sinica, 2008, 24, 637–644. DOI: 10.1007/s10409-008-0185-7.
27. Nádai, A. Plasticity: A Mechanics of the Plastic State of Matter, 4^th ed., McGraw-Hill, 1931, 349 p.
28. Poole, R.J. The Deborah and Weissenberg numbers. In: The British Society of Rheology, Rheology Bulletin, 2012, 53 (2), 32–39.
28. Prosviryakov, E.Yu. A new class of exact solutions to the Navier-Stokes equations with the Boussinesq approximation for describing convective flows of multilayer fluids. Fluid Dynamics, 2020, 55 (6), 798–809.
28. Rajagopal, K.R. On boundary conditions for fluids of the differential type. In: Sequeira, A., ed., Navier-Stokes equations and related nonlinear problems, Springer, Boston, MA, 1995. DOI: 10.1007/978-1-4899-1415-6_22.
28. Rao, I.J. and Rajagopal, K.R. The effect of the slip boundary condition on the flow of fluids in a channel. Acta Mechanica, 1999, 135, 113–126. DOI: 10.1007/BF01305747.
28. Sofonea, M. and Matei, A. Variational Inequalities with Applications: A Study of Antiplane Frictional Contact Problems, Springer, 2009, 230 p.
28. Truesdell, C. and Noll, W. The Non-Linear Field Theories of Mechanics, 3rd ed., Springer, 2004, 602 p.
    Vinogradov, G.V. and Malkin, A.Y. Rheology of Polymers: Viscoelasticity and Flow of Polymers, Springer, 1980, 468 p.
    Whiteman, J.R., ed. The Mathematics of Finite Elements and Applications: Mafelap 1984, Academic Press, 1985, 650 p.
36. Yih, C.-S. Dynamics of Nonhomogeneous Fluids, Macmillan, 1965, 306 p.
37. Wilson, S.D.R. The drag-out problem in film coating theory. Journal of Engineering Mathematics, 1982, 16, 209–221. DOI; 10.1007/BF00042717.
38. Prosviryakov, E.Yu., Ledyankina, O.A., and Goruleva, L.S. A class of exact solutions of magnetic hydrodynamics equations for describing convective flows of multilayer fluids. Russian Aeronautics, 2024, 67, 550–563. DOI: 10.3103/S1068799824030103.
39. Prosviryakov, E.Yu., Ledyankina, O.A., and Goruleva, L.S. Exact solutions of the Oberbeck-Boussinesq equations for describing the creeping flows of multicomponent fluids. Procedia Structural Integrity, 2024, 65, 177–184. DOI: 10.1016/j.prostr.2024.11.028.

1. Скульский О. И., Аристов С. Н. Механика аномально вязких – М. ; Ижевск : РХД, 2004. – 154 с.
2. Aristov S. N., Skulskii O. I. Exact solution of the problem on a six‐constant Jeffreys model of fluid in a plane channel // Journal of Applied Mechanics and Technical Physics. – 2002. – Vol. 43. – P. 817–822. – DOI: 10.1023/A:1020752101539.
3. Aristov S. N., Skulskiy O. I. Viscoelastic effects of blood flow in nondeformable // Russian Journal of Biomechanics. – 1999. – Vol. 3 (4). – P. 24–33.
4. Chhabra R. P., Richardson J. F. Non‐Newtonian Flow in the Process Industries: Fundamentals and Engineering Applications. – 1st ed. – Oxford, UK : Butterworth‐Heinemann, 1999. – 436 p.
5. Middleman S. Fundamentals of Polymer Processing. – McGraw-Hill, 1977. – 525 p.
6. Bird R. B., Armstrong R. C., Hassager O. Dynamics of Polymeric Liquids. Vol. 1. Fluid Mechanics. – 2nd ed. – Wiley, 1987. – 672 p.
7. Tanner R. I. Engineering Rheology. – 2nd ed. – OUP Oxford University Press, 2000. – 586 p.
8. Schowalter W. R. Mechanics of Non-Newtonian Fluids. – Pergamon Press, 1978. – 300 p.
9. Hartnett J. P., Kostic M. Heat transfer to a viscoelastic fluid in laminar flow through a rectangular channel // International Journal of Heat and Mass Transfer. – 1985. – Vol. 28 (6). – P. 1147–1155. – DOI: 10.1016/0017-9310(85)90122-X.
10. Aristov S. N., Keller I. E. Beltrami stress fields in an elastic body // Doklady Physics. – 2016. – Vol. 61 (7). – P. 343–346. – DOI: 10.1134/S1028335816070065.
11. Gubareva K. V., Prosviryakov E. Yu. Exact analytical solution to the problem of stationary convection in the Boussinesq approximation with account for viscous dissipation // Diagnostics, Resource and Mechanics of materials and structures. – 2025. – Iss. 6. – P. 23–38. – DOI: 10.17804/2410-9908.2025.6.023-038. – URL: http://dream-journal.org/issues/2025-6/2025-6_528.html
12. Towards understanding the algorithms for solving the Navier-Stokes equations / S. V. Ershkov, E. Yu. Prosviryakov, N. V. Burmasheva, V. Christianto // Fluid Dynamics Research. – 2021. – Vol. 53 (4). – P. 044501. – DOI: 10.1088/1873-7005/ac10f0.
13. Exact solutions of the Oberbeck-Boussinesq equations for the description of shear thermal diffusion of Newtonian fluid flows / S. Ershkov, N. Burmasheva, D. D. Leshchenko, E. Yu. Prosviryakov // Symmetry. – 2023. – Vol. 15 (9). – P. 1730. – DOI: 10.3390/sym15091730.
14. Solving the hydrodynamical system of equations of inhomogeneous fluid flows with thermal diffusion: a review / S. V. Ershkov, E. Yu. Prosviryakov, N. V. Burmasheva, V. Christianto // Symmetry. – 2023. – Vol. 15. – P. 1825. – DOI: 10.3390/sym15101825.
15. Gubareva K. V., Prosviryakov E. Yu., Eremin A. V. An exact solution with inhomogeneous boundary conditions for a steady non-uniform Couette flow between permeable plates // Diagnostics, Resource and Mechanics of materials and structures. – 2025. – Iss. 5. – P. 66–86. – DOI: 10.17804/2410-9908.2025.5.066-086. – URL: http://dream-journal.org/issues/2025-5/2025-5_522.html
16. Chang H.-C., Demekhin E. A. Studies in Interface Science. Vol. 14. Complex Wave Dynamics on Thin Films. – Elsevier, 2002. – 412 p.
17. Falling Liquid Films / S. Kalliadasis, C. Ruyer-Quil, B. Scheid, M. G. Velarde. Series Applied Mathematical Sciences. – London : Springer, 2012. – DOI: 10.1007/978-1-84882-367-9.
18. Baranovskii E. S., Prosviryakov E. Yu., Ershkov S. V. Mathematical analysis of steady non-isothermal flows of a micropolar fluid // Nonlinear Analysis: Real World Applications. – 2025. – Vol. 84. – P. 104294. – DOI: 10.1016/j.nonrwa.2024.104294.
19. Non-Newtonian rivulet-flows on unsteady heated plane surface / S. V. Ershkov, E. S. Baranovskii, E. Yu. Prosviryakov, A. V. Yudin // International Journal of Non-Linear Mechanics. – 2025. – Vol. 170. – P. 104984. – DOI: 10.1016/j.ijnonlinmec.2024.104984.
20. Gubareva K. V., Prosviryakov E. Yu., Eremin A. V. Inhomogeneous Couette–Poiseuille flow of a viscous incompressible fluid in an infinite horizontal layer with permeable boundaries // Diagnostics, Resource and Mechanics of materials and structures. – 2025. – Iss. 5. – P. 6–28. – DOI: 10.17804/2410-9908.2025.5.006-028. – URL: http://dream-journal.org/issues/2025-5/2025-5_523.html
21. Baranovskii E. S. Analytical Solutions to the unsteady Poiseuille flow of a second grade fluid with slip boundary conditions // Polymers. – 2024. – Vol. 16 (2). – P. 179. – DOI: 10.3390/polym16020179.
22. Denier J. P., Dabrowski P. P. On the boundary-layer equations for power-law fluids // Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. – 2004. – Vol. 460. – P. 3143–3158. – DOI: 10.1098/rspa.2004.1349.
23. Frigaard I. A., Ryan D. P. Flow of a viscoplastic fluid in a channel of slowly varying width // Journal of Non-Newtonian Fluid Mechanics. – 2004. – Vol. 123 (1). – P. 67–83. – DOI: 10.1016/j.jnnfm.2004.06.011.
24. Málek J., Rajagopal K. R., Růžička M. Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity // Mathematical Models and Methods in Applied Sciences. – 1995. – Vol. 05 (06). – P. 789–812. – DOI: 10.1142/S0218202595000449.
25. Massoudi M., Phuoc T. X. Fully developed flow of a modified second grade fluid with temperature dependent viscosity // Acta Mechanica. – 2001. – Vol. 150. – P. 23–37. – DOI: 10.1007/BF01178542.
26. Mekheimer Kh. S., El Kot M. A. The micropolar fluid model for blood flow through a tapered artery with a stenosis // Acta Mechanica Sinica. – 2008. – Vol. 24. – P. 637–644. – DOI: 10.1007/s10409-008-0185-7.
27. Nádai A. Plasticity: A Mechanics of the Plastic State of Matter. – 4th ed. – McGraw-Hill, 1931. – 349 p.
28. Poole R. J. The Deborah and Weissenberg numbers // Rheology Bulletin. – 2012. – 53 (2). – P. 32–39.
29. Prosviryakov E. Yu. A new class of exact solutions to the Navier-Stokes equations with the Boussinesq approximation for describing convective flows of multilayer fluids // Fluid Dynamics. – 2020. – Vol. 55 (6). – P. 798–809.
30. Rajagopal K. R. On boundary conditions for fluids of the differential type // Navier-Stokes equations and related nonlinear problems / ed. by A. Sequeira. – Boston, MA : Springer, 1995. – P. 273–278. – DOI: 10.1007/978-1-4899-1415-6_22.
31. Rao I. J., Rajagopal K. R. The effect of the slip boundary condition on the flow of fluids in a channel // Acta Mechanica. – 1999. – Vol. 135. – P. 113–126. – DOI: 10.1007/BF01305747.
32. Sofonea M., Matei A. Variational Inequalities with Applications: A Study of Antiplane Frictional Contact Problems. – Springer, 2009. – 230 p.
33. Truesdell C., Noll W. The Non-Linear Field Theories of Mechanics. – 3rd ed. – Springer, 2004. – 602 p.
34. Vinogradov G. V., Malkin A. Y. Rheology of Polymers. Viscoelasticity and Flow of Polymers. – Springer, 1980. – 468 p.
35. The Mathematics of Finite Elements and Applications: Mafelap 1984 / ed. by J. R. Whiteman. – Academic Press, 1985. – 650 p.
36. Yih, C.-S. Dynamics of Nonhomogeneous Fluids. – Macmillan, 1965. – 306 p.
37. Wilson S. D. R. The drag-out problem in film coating theory // Journal of Engineering Mathematics. – 1982. – Vol. 16. – P. 209–221. – DOI; 10.1007/BF00042717.
38. Prosviryakov E. Yu., Ledyankina O. A., Goruleva L. S. A class of exact solutions of magnetic hydrodynamics equations for describing convective flows of multilayer fluids // Russian Aeronautics. – 2024. – Vol. 67. – P. 550–563. – DOI: 10.3103/S1068799824030103.
39. Prosviryakov E. Yu., Ledyankina O. A., Goruleva L. S. Exact solutions of the Oberbeck–Boussinesq equations for describing the creeping flows of multicomponent fluids // Procedia Structural Integrity. – 2024. – Vol. 65. – P. 177–184. – DOI: 10.1016/j.prostr.2024.11.028.

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