Samokhin, Vjacheslav Nicolaevich

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Total publications: 22
Scientific articles: 22

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Samokhin, Vjacheslav Nicolaevich
Doctor of physico-mathematical sciences (1999)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 10.04.1945
Keywords: partial differential equations; non-linear differential equations; Navier–Stokes system; boundary layer theory; Prandtl system; hydrodynamics of non-Newtonian fluids; magnetohydrodynamics.


The existence of a solution of a system of boundary layer equations that arise in the hydrodynamics of a non-Newtonian liquid is proved. It is established that the rate of propagation of the perturbations is finite under particular conditions. The existence of the solution of basic boundary problems and initial-boundary value problems for systems of magnetohydrodynamics of pseudoplastic and dilatantous media is proved. It is solved some free boundary problems of non-Newtonian and conducting fluids. The method of homogenization for the boundary layer equations with a rapidly oscillating parameter is applied.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1968 (department of differential equations). Ph. D. thesis was defended in 1973. D. Sci. thesis was defended in 1999. A list of my works contains more than 127 titles.
Soros Associate Professor — 1997 and 1999. Soros Professor — 2001.

Main publications:
  1. Samokhin V. N., “Obobschennye resheniya zadachi o prodolzhenii pogranichnogo sloya psevdoplasticheskoi zhidkosti”, Trudy sem. im. I. G. Petrovskogo, 3, 1978, 161–175  mathscinet  zmath
  2. Samokhin V. N., “O sisteme uravnenii magnitogidrodinamicheskogo pogranichnogo sloya dilatantnoi sredy”, Differents. uravneniya, 29:2 (1993), 328–336  mathscinet  zmath
  3. Samokhin V. N., “Suschestvovanie resheniya odnoi modifikatsii sistemy uravnenii magnitnoi gidrodinamiki”, Matem. sb., 182:3 (1991), 395–407  mathnet  mathscinet  zmath
  4. Samokhin V. N., “Ob odnom klasse uravnenii, obobschayuschikh uravneniya politropnoi filtratsii”, Differents. uravneniya, 32:5 (1996), 643–651  mathscinet  zmath
  5. Oleinik O. A., Samokhin V. N., Mathematical models in boundary layer theory, Chapman & Hall / CRC, Boca Raton, FL, 1999  mathscinet  zmath
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. R. R. Bulatova, V. N. Samokhin, G. A. Chechkin, “Equations of symmetric MHD-boundary layer of viscous fluid with Ladyzhenskaya rheology law”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019),  72–90  mathnet; J. Math. Sci. (N. Y.), 244:2 (2020), 158–169  scopus
2. V. N. Samokhin, G. A. Chechkin, “Equations of boundary layer for a generalized newtonian medium near a critical point”, Tr. Semim. im. I. G. Petrovskogo, 31 (2016),  158–176  mathnet; J. Math. Sci. (N. Y.), 234:4 (2018), 485–496  scopus
3. V. N. Samokhin, G. M. Fadeeva, G. A. Chechkin, “Equations of the boundary layer for a modified Navier-Stokes system”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011),  329–361  mathnet  zmath  elib; J. Math. Sci. (N. Y.), 179:4 (2011), 557–577  scopus
4. V. N. Samokhin, “Boundary Layer Formation in a Pseudoelastic Medium Under Gradual Acceleration”, Differ. Uravn., 40:3 (2004),  406–416  mathnet  mathscinet; Differ. Equ., 40:3 (2004), 438–450
5. V. N. Samokhin, “The operator form and the solvability of magnetohydrodynamic equations for nonlinearly viscous media”, Differ. Uravn., 36:6 (2000),  816–821  mathnet  mathscinet; Differ. Equ., 36:6 (2000), 904–910
6. V. N. Samokhin, “Equations of a magnetohydrodynamic boundary layer with diffraction conditions”, Differ. Uravn., 33:8 (1997),  1106–1113  mathnet  mathscinet; Differ. Equ., 33:8 (1997), 1113–1120
7. V. N. Samokhin, “On a class of equations that generalize equations of polytropic filtration”, Differ. Uravn., 32:5 (1996),  643–651  mathnet  mathscinet; Differ. Equ., 32:5 (1996), 648–657
8. V. N. Samokhin, “On the equations of polytropic filtration with a variable non-linearity”, Uspekhi Mat. Nauk, 49:3(297) (1994),  189–190  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:3 (1994), 196–197  isi
9. V. N. Samokhin, “On a system of equations of a magnetohydrodynamic boundary layer of a dilatant medium”, Differ. Uravn., 29:2 (1993),  328–336  mathnet  mathscinet; Differ. Equ., 29:2 (1993), 270–277
10. V. N. Samokhin, “On the system of equations of the laminar boundary layer in the presence of injection of a non-Newtonian fluid”, Sibirsk. Mat. Zh., 34:1 (1993),  157–168  mathnet  mathscinet  zmath; Siberian Math. J., 34:1 (1993), 139–149  isi
11. V. N. Samokhin, “On a problem with an unknown boundary in the hydrodynamics of electrically conducting media”, Uspekhi Mat. Nauk, 47:3(285) (1992),  173–174  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:3 (1992), 188–189  isi
12. V. N. Samokhin, “On a system of equations in the magnetohydrodynamics of nonlinearly viscous media”, Differ. Uravn., 27:5 (1991),  886–896  mathnet  mathscinet; Differ. Equ., 27:5 (1991), 628–636
13. V. N. Samokhin, “Existence of a solution of a modification of a system of equations of magnetohydrodynamics”, Mat. Sb., 182:3 (1991),  395–407  mathnet  mathscinet  zmath; Math. USSR-Sb., 72:2 (1992), 373–385  isi
14. V. N. Samokhin, “Averaging of a system of Prandtl equations”, Differ. Uravn., 26:3 (1990),  495–501  mathnet  mathscinet; Differ. Equ., 26:3 (1990), 369–374
15. V. N. Samokhin, “Generalized solutions of a system of equations of the boundary layer of dilatant fluids, and the finite rate of perturbations”, Differ. Uravn., 23:6 (1987),  1053–1061  mathnet  mathscinet
16. V. N. Samokhin, “A diffraction problem for strongly nonlinear equations”, Mat. Zametki, 42:2 (1987),  256–261  mathnet  mathscinet  zmath; Math. Notes, 42:2 (1987), 645–648  isi
17. V. N. Samokhin, “On a system of boundary-layer equations of dilatant fluids”, Uspekhi Mat. Nauk, 41:5(251) (1986),  195–196  mathnet  mathscinet; Russian Math. Surveys, 41:5 (1986), 163–164  isi
18. V. N. Samokhin, “Laminar mixing layer on the boundary of two flows”, Zh. Vychisl. Mat. Mat. Fiz., 25:4 (1985),  614–617  mathnet  mathscinet; U.S.S.R. Comput. Math. Math. Phys., 25:2 (1985), 186–188
19. V. N. Samokhin, “Asymptotic expansions for the problem of boundary layer formation”, Zh. Vychisl. Mat. Mat. Fiz., 22:5 (1982),  1260–1265  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 22:5 (1982), 255–261
20. V. N. Samokhin, “The system of equations of a boundary layer of a pseudoplastic fluid”, Dokl. Akad. Nauk SSSR, 210:5 (1973),  1043–1046  mathnet  mathscinet
21. V. N. Samokhin, “Development of a plane-parallel symmetric boundary layer when a sudden motion arises”, Tr. Mosk. Mat. Obs., 28 (1973),  117–133  mathnet  mathscinet  zmath
22. V. N. Samokhin, “Equations for the boundary layer for a pseudoplastic fluid in the neighborhood of a stopping point”, Uspekhi Mat. Nauk, 27:6(168) (1972),  249–250  mathnet  mathscinet  zmath

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