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Plotnikov, Pavel Igorevich
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences (1987)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: ;

https://www.mathnet.ru/eng/person21099
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/206683

Publications in Math-Net.Ru Citations
2023
1. P. I. Plotnikov, J. Sokolowski, “Gradient flows in the shape optimization theory”, Dokl. RAN. Math. Inf. Proc. Upr., 513 (2023),  71–75  mathnet  elib; Dokl. Math., 108:2 (2023), 387–391 1
2021
2. P. I. Plotnikov, “Mathematical modeling of neo-Hookean material growth”, Dokl. RAN. Math. Inf. Proc. Upr., 501 (2021),  74–78  mathnet  zmath  elib; Dokl. Math., 104:3 (2021), 380–384  scopus 1
3. P. I. Plotnikov, “Modeling the isotropic growth of incompressible neo-Hookean material”, Sib. Zh. Ind. Mat., 24:4 (2021),  97–110  mathnet 1
2020
4. P. I. Plotnikov, “Concentrations problem for solutions to compressible Navier–Stokes equations”, Dokl. RAN. Math. Inf. Proc. Upr., 495 (2020),  55–58  mathnet  zmath  elib; Dokl. Math., 102:3 (2020), 493–496
5. P. I. Plotnikov, “Volumetric growth of neo-Hookean incompressible material”, Sib. Èlektron. Mat. Izv., 17 (2020),  1990–2027  mathnet 1
6. P. I. Plotnikov, J. Sokołowski, “Dynamics of a Crankshaft Mechanism under the Pressure of a Viscous Gas”, Trudy Mat. Inst. Steklova, 310 (2020),  237–266  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 310 (2020), 220–249  isi  scopus
2019
7. M. Yu. Mamatyukov, A. K. Khe, D. V. Parshin, P. I. Plotnikov, A. P. Chupakhin, “On the energy of a hydroelastic system: blood flow in an artery with cerebral aneurysm”, Prikl. Mekh. Tekh. Fiz., 60:6 (2019),  3–16  mathnet  elib; J. Appl. Mech. Tech. Phys., 60:6 (2019), 977–988 6
2017
8. W. Weigant, P. I. Plotnikov, “Bounds for solutions of isothermal equations of viscous gas dynamics”, Mat. Sb., 208:8 (2017),  31–55  mathnet  mathscinet  zmath  elib; Sb. Math., 208:8 (2017), 1113–1137  isi  scopus 1
9. W. Weigant, P. I. Plotnikov, “Rotationally symmetric viscous gas flows”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017),  382–395  mathnet  elib; Comput. Math. Math. Phys., 57:3 (2017), 387–400  isi  scopus 2
2013
10. P. I. Plotnikov, S. A. Sazhenkov, “Kinetic equation method for problems of viscous gas dynamics with rapidly oscillating density distributions”, Trudy Mat. Inst. Steklova, 281 (2013),  68–83  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 281 (2013), 62–76  isi  elib
2008
11. P. I. Plotnikov, I. V. Kuznetsov, “On equations of motion of a nonlinear hydroelastic structure”, Prikl. Mekh. Tekh. Fiz., 49:4 (2008),  174–191  mathnet  elib; J. Appl. Mech. Tech. Phys., 49:4 (2008), 666–680 1
2007
12. P. I. Plotnikov, J. Sokolowski, “Stationary solutions of Navier–Stokes equations for diatomic gases”, Uspekhi Mat. Nauk, 62:3(375) (2007),  117–148  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 62:3 (2007), 561–593  isi  elib  scopus 47
2006
13. P. I. Plotnikov, “Analytical extension of a solution to Mac-Leod equation”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 6:2 (2006),  67–75  mathnet
2001
14. P. I. Plotnikov, A. V. Klepacheva, “The phase field equations and gradient flows of marginal functions”, Sibirsk. Mat. Zh., 42:3 (2001),  651–669  mathnet  mathscinet  zmath; Siberian Math. J., 42:3 (2001), 551–567  isi 15
2000
15. S. Luckhaus, P. I. Plotnikov, “Entropy solutions of Buckley–Leverett equations”, Sibirsk. Mat. Zh., 41:2 (2000),  400–420  mathnet  mathscinet  zmath; Siberian Math. J., 41:2 (2000), 329–348 15
1997
16. P. I. Plotnikov, “Passage to the limit with respect to a small parameter in Cahn–Hilliard equations”, Sibirsk. Mat. Zh., 38:3 (1997),  638–656  mathnet  mathscinet  zmath; Siberian Math. J., 38:3 (1997), 550–566  isi 9
1996
17. P. I. Plotnikov, “Forward-backward parabolic equations and hysteresis”, Zap. Nauchn. Sem. POMI, 233 (1996),  183–209  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 93:5 (1999), 747–766 20
1995
18. P. I. Plotnikov, “On a certain class of curves arising in a free boundary problem for Stokes flows”, Sibirsk. Mat. Zh., 36:3 (1995),  619–627  mathnet  mathscinet  zmath; Siberian Math. J., 36:3 (1995), 533–540  isi 1
19. P. I. Plotnikov, L. V. Shurshalov, “On the nature of intensive interaction between a cloud of interplanetary dust particles and the Earth's atmosphere”, Zh. Vychisl. Mat. Mat. Fiz., 35:8 (1995),  1233–1244  mathnet 3
1994
20. P. I. Plotnikov, “Passage to the limit with respect to viscosity in an equation with a variable direction of parabolicity”, Differ. Uravn., 30:4 (1994),  665–674  mathnet  mathscinet; Differ. Equ., 30:4 (1994), 614–622 1
21. P. I. Plotnikov, “Morse theory for conditionally-periodic solutions to Hamiltonian systems”, Sibirsk. Mat. Zh., 35:3 (1994),  657–673  mathnet  mathscinet  zmath; Siberian Math. J., 35:3 (1994), 590–604  isi 2
1993
22. P. I. Plotnikov, “Equations with a variable direction of parabolicity and the hysteresis effect”, Dokl. Akad. Nauk, 330:6 (1993),  691–693  mathnet  mathscinet  zmath; Dokl. Math., 47:3 (1993), 604–608 2
23. P. I. Plotnikov, V. N. Starovoitov, “The Stefan problem with surface tension as a limit of the phase field model”, Differ. Uravn., 29:3 (1993),  461–471  mathnet  mathscinet; Differ. Equ., 29:3 (1993), 395–404 17
24. P. I. Plotnikov, “Generalized solutions to a free boundary problem of motion of a non-newtonian fluid”, Sibirsk. Mat. Zh., 34:4 (1993),  127–141  mathnet  mathscinet  zmath; Siberian Math. J., 34:4 (1993), 704–716  isi 18
1991
25. P. I. Plotnikov, “Nonuniqueness of solutions of the problem of solitary waves and bifurcation of critical points of smooth functionals”, Izv. Akad. Nauk SSSR Ser. Mat., 55:2 (1991),  339–366  mathnet  mathscinet  zmath; Math. USSR-Izv., 38:2 (1992), 333–357  isi 24
1988
26. P. I. Plotnikov, L. N. Yungerman, “Periodic solutions of a weakly nonlinear wave equation with an irrational relation of period to interval length”, Differ. Uravn., 24:9 (1988),  1599–1607  mathnet  mathscinet; Differ. Equ., 24:9 (1988), 1059–1065 1
27. P. I. Plotnikov, “Existence of a countable set of periodic solutions of the problem of forced oscillations for a weakly nonlinear wave equation”, Mat. Sb. (N.S.), 136(178):4(8) (1988),  546–560  mathnet  mathscinet  zmath; Math. USSR-Sb., 64:2 (1989), 543–556 20
1983
28. P. I. Plotnikov, “Justification of the Stokes hypothesis in the theory of surface waves”, Dokl. Akad. Nauk SSSR, 269:1 (1983),  80–83  mathnet  mathscinet  zmath
1980
29. P. I. Plotnikov, “Solvability of the problem of spatial gravitational waves on the surface of an ideal fluid”, Dokl. Akad. Nauk SSSR, 251:3 (1980),  591–594  mathnet  mathscinet  zmath
30. V. N. Monakhov, P. I. Plotnikov, “Quasiconformal mappings and problems in hydrodynamics”, Prikl. Mekh. Tekh. Fiz., 21:5 (1980),  59–69  mathnet; J. Appl. Mech. Tech. Phys., 21:5 (1980), 624–632
31. P. I. Plotnikov, “Incorrectness of a non-linear problem on development of the Taylor instability”, Zap. Nauchn. Sem. LOMI, 96 (1980),  240–246  mathnet  mathscinet  zmath; J. Soviet Math., 21:5 (1983), 824–829 2
1979
32. P. I. Plotnikov, “Existence of space waves on the surface of ideal fluid”, Zap. Nauchn. Sem. LOMI, 84 (1979),  211–219  mathnet  mathscinet  zmath; J. Soviet Math., 21:3 (1983), 399–405
1975
33. P. I. Plotnikov, “Spatial potential flows with free boundary”, Dokl. Akad. Nauk SSSR, 224:6 (1975),  1287–1289  mathnet  mathscinet  zmath
2000
34. M. M. Lavrent'ev, V. L. Beresnev, A. A. Borovkov, S. K. Godunov, S. S. Goncharov, Yu. L. Ershov, S. S. Kutateladze, P. I. Plotnikov, Yu. G. Reshetnyak, V. G. Romanov, “Mikhail Alekseevich Lavrent'ev (on the centenary of his birth)”, Sibirsk. Mat. Zh., 41:5 (2000),  969–983  mathnet  mathscinet  zmath 1

Presentations in Math-Net.Ru
1. Mathematical aspects of brain growth modeling
P. I. Plotnikov
Dynamics days in Sirius. On the occasion of academician Dmitry V. Treschev’s anniversary
October 29, 2024 09:30
2. Краевые задачи для уравнений Навье—Стокса и Навье—Стокса—Пуассона динамики вязкого газа
P. I. Plotnikov
Conference dedicated to 70th anniversary of A. L. Skubachevsky
December 14, 2023 15:00
3. Градиентные потоки в теории оптимизации формы
P. I. Plotnikov
International Conference "Mathematical Methods of Mechanics" dedicated to the anniversary of academician A. G. Kulikovskii
March 22, 2023 10:00   
4. Weak solutions to 2D and 3D compressible Navier-Stokes equations in critical case
Pavel Plotnikov
Mathematical Aspects of Contemporary Continuum Mechanics
November 12, 2021 10:30   
5. Stokes waves of extreme form
P. I. Plotnikov
Complex Approximations, Orthogonal Polynomials and Applications Workshop
June 10, 2021 17:00
6. Variational methods of conformal geometry in mathematical physics.
P. I. Plotnikov
International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday
January 23, 2020 15:00   
7. Variational problems of conformal geometry and hydroelastic waves
P. I. Plotnikov
Dynamics in Siberia - 2018
February 28, 2018 11:50
8. Объемный рост материалов. Математическая теория
P. I. Plotnikov
Seminar of the Department of Mechanics
May 16, 2016 12:00
9. Lower dimensional tori in Hamiltonian systems. Variational approach
P. I. Plotnikov, I. V. Kuznetsov
International scientific conference "Days of Classical Mechanics"
January 26, 2015 11:25   
10. Boundary value problems for compressible Navier-Stokes equations
P. I. Plotnikov, W. Weigant
The Seventh International Conference on Differential and Functional Differential Equations
August 25, 2014 10:55

Organisations
 
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