Vedenyapin, Victor Valentinovich

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Total publications: 46
Scientific articles: 46
Presentations: 23

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Doctor of physico-mathematical sciences (1990)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 22.07.1949
E-mail: , ,
Keywords: kinetic equations; Boltzmann equation; Vlasov equation; entropy; Quantum Hamiltonians.


For the Boltzmann and free motion Kinetik Equations klassification of conserving and decreasing functional is proposed. A theorem on the Uniqueness of the Boltzmann H-function is proved: For the Gaz deskribed by the Boltzmann Kinetic Equation Entropy is the Unique functional decreasing in time. A problem of calculation in explicit form of coefficients for Boltzmann equationin in the case of maxwellian molecules is solved, complete number of integrals is written. First descrete velocity models with proper invariants are constructed for Mixtures, in one dimentional case the unique model is found. Asimptotics of spectrum for a certain class of quantum optic Hamiltonians is found, special polinomials are introduced. Representation of general commutative relations are classified. General correspondence principle "Quantum Hamiltonians–Kinetic Equations" is constructed that generalize Landau–Lifshits–Streater correspondence. General theory of conservational laws for quantum hamiltonians and kinetic equations is constructed, that corresponds each other.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1971 (department of differential geometry). Ph.D. thesis was defended in 1977. D.Sci. thesis was defended in 1989. A list of my works contains more than 50 titles. Since 1992 I and M. V. Maslennicov and V. A. Dorodnitsyn have led the research seminar at the Keldysh Institute of Applied Mathematics on mathematical physics. Professor of Moscow University of Physics and Technology since 1992.

USSR State Prise winner (1989) "For Mathematical Methods in Boltzmann Equation".

Main publications:
  • On the Connection of the Formulas for Entropy and Stationary Distribution // Journal of Statistical Physics, 1994, vol. 77, no. 5/6 (with Y. Arhipov and A. Klar).
  • Velocity Inductive Construction for Mixtures // Transport theory and Statistical Physics, 1999, 28(7), 727–742.
  • Special Polinomials in Problems of Quantum Optics // Modern Physics Letters B, 1995, vol. 9, no. 5, 291–298 (with Yu. Orlov).
  • A class of Invariants for the Boltzmann equation and the Broadwell model // Eur. Jour. Mech., B/Fluids, 1997, no. 3, 387–399 (with Y. Arhipov, A. Klar, O. Mingalev).
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. V. Vedenyapin, N. S. Smirnova, “Euler and Navier–Stokes equations as self-consistent fields”, Keldysh Institute preprints, 2019, 041, 20 pp.  mathnet  elib
2. V. V. Vedenyapin, I. S. Pershin, “Vlasov–Maxwell–Einstein equation and Einstein lambda”, Keldysh Institute preprints, 2019, 039, 17 pp.  mathnet
3. V. V. Vedenyapin, N. I. Karavaeva, O. A. Kostiuk, B. N. Chetverushkin, “Schrödinger equation as a consequence of new Vlasov type equations”, Keldysh Institute preprints, 2019, 026, 11 pp.  mathnet  elib
4. S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties”, Nanosystems: Physics, Chemistry, Mathematics, 10:5 (2019),  549–563  mathnet  isi
5. V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Уравнение типа Власова–Максвелла–Эйнштейна и переход к слаборелятивистскому приближению”, Zh. Vychisl. Mat. Mat. Fiz., 59:11 (2019),  1883–1898  mathnet  elib
6. V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Entropy in the sense of Boltzmann and Poincare, Boltzmann extremals, and the Hamilton–Jacobi method in non-Hamiltonian context”, CMFD, 64:1 (2018),  37–59  mathnet
7. V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “On the Vlasov–Maxwell–Einstein equation and its non-relativistic and weakly relativistic analogues”, Keldysh Institute preprints, 2018, 265, 30 pp.  mathnet  elib
8. V. V. Vedenyapin, “Vlasov–Maxwell–Einstein Equation”, Keldysh Institute preprints, 2018, 188, 20 pp.  mathnet  elib
9. S. Z. Adzhiev, V. V. Vedenyapin, S. S. Filippov, “$H$-theorem for continuous- and discrete-time chemical kinetic systems and a system of nucleosynthesis equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:9 (2018),  1517–1530  mathnet  elib; Comput. Math. Math. Phys., 58:9 (2018), 1462–1476  isi  scopus
10. V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. RAN. Ser. Mat., 81:3 (2017),  45–82  mathnet  mathscinet  elib; Izv. Math., 81:3 (2017), 505–541  isi  scopus
11. S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Zh. Vychisl. Mat. Mat. Fiz., 57:12 (2017),  2065–2078  mathnet  elib; Comput. Math. Math. Phys., 57:12 (2017), 2017–2029  isi  scopus
12. V. V. Vedenyapin, N. N. Fimin, “Hamilton–Jacobi method for non-Hamiltonian systems”, Keldysh Institute preprints, 2015, 013, 18 pp.  mathnet
13. V. V. Vedenyapin, N. N. Fimin, “The Hamilton – Jacobi method for non-Hamiltonian systems”, Nelin. Dinam., 11:2 (2015),  279–286  mathnet
14. V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Uspekhi Mat. Nauk, 69:6(420) (2014),  45–80  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 69:6 (2014), 995–1029  isi  scopus
15. V. V. Vedenyapin, M. A. Negmatov, “On derivation and classification of Vlasov type equations and equations of magnetohydrodynamics. The Lagrange identity, the Godunov form, and critical mass”, CMFD, 47 (2013),  5–17  mathnet; Journal of Mathematical Sciences, 202:5 (2014), 769–782  scopus
16. V. V. Vedenyapin, M. A. Negmatov, “Derivation and classification of Vlasov-type and magnetohydrodynamics equations: Lagrange identity and Godunov's form”, TMF, 170:3 (2012),  468–480  mathnet  mathscinet  elib; Theoret. and Math. Phys., 170:3 (2012), 394–405  isi  elib  scopus
17. S. Z. Adzhiev, V. V. Vedenyapin, “Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model”, Zh. Vychisl. Mat. Mat. Fiz., 51:11 (2011),  2063–2074  mathnet  mathscinet; Comput. Math. Math. Phys., 51:11 (2011), 1942–1952  isi  scopus
18. V. V. Vedenyapin, “Time averages and Boltzmann extremals”, Dokl. Akad. Nauk, 422:2 (2008),  161–163  mathnet  mathscinet  zmath; Dokl. Math., 78:2 (2008), 686–688  scopus
19. S. Z. Adzhiev, V. V. Vedenyapin, “On the sizes of discrete velocity models of the Boltzmann equation for mixtures”, Zh. Vychisl. Mat. Mat. Fiz., 47:6 (2007),  1045–1054  mathnet  elib; Comput. Math. Math. Phys., 47:6 (2007), 998–1006  elib  scopus
20. V. V. Vedenyapin, “Photophoresis and reactive forses”, Matem. Mod., 18:8 (2006),  77–85  mathnet  zmath
21. Ya. G. Batishcheva, V. V. Vedenyapin, “The 2-nd low of thermodynamics for chemical kinetics”, Matem. Mod., 17:8 (2005),  106–110  mathnet  mathscinet  zmath
22. S. Z. Adzhiev, S. A. Amosov, V. V. Vedenyapin, “One-dimensional discrete models of kinetic equations for mixtures”, Zh. Vychisl. Mat. Mat. Fiz., 44:3 (2004),  553–558  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 44:3 (2004), 523–528
23. V. V. Vedenyapin, Ya. G. Batishcheva, I. V. Melikhov, A. Ya. Gorbatchevski, “On the motion of solids in gas with nonuniform surface chemical processes”, Matem. Mod., 15:6 (2003),  6–10  mathnet  zmath
24. V. V. Vedenyapin, S. A. Amosov, “Discrete models of the Boltzmann equation for mixtures”, Differ. Uravn., 36:7 (2000),  925–929  mathnet  mathscinet; Differ. Equ., 36:7 (2000), 1027–1032
25. V. V. Vedenyapin, S. A. Amosov, L. Toscano, “Discrete velocity models of Boltzmann equation for mixtures”, Matem. Mod., 12:7 (2000),  18–22  mathnet  mathscinet  zmath
26. V. V. Vedenyapin, “Discrete Velocity Models for Mixtures”, Keldysh Institute preprints, 1999, 017  mathnet
27. V. V. Vedenyapin, S. A. Amosov, L. Toscano, “Invariants for Hamiltonians and kinetic equations”, Uspekhi Mat. Nauk, 54:5(329) (1999),  153–154  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 54:5 (1999), 1056–1057  isi  scopus
28. V. V. Vedenyapin, Yu. N. Orlov, “Conservation laws for polynomial Hamiltonians and for discrete models of the Boltzmann equation”, TMF, 121:2 (1999),  307–315  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 121:2 (1999), 1516–1523  isi
29. V. V. Vedenyapin, O. V. Mingalev, “Representations of general commutation relations. Asymptotics of the spectrum of three quantum Hamiltonians”, Dokl. Akad. Nauk, 352:2 (1997),  155–158  mathnet  mathscinet  zmath
30. S. A. Amossov, V. V. Vedenyapin, “On the Vlasov-Einstein Equation and Quantization of Vlasov Equation”, Keldysh Institute preprints, 1997, 013  mathnet
31. V. V. Vedenyapin, O. V. Mingalev, I. V. Mingalev, “Representations of general commutation relations”, TMF, 113:3 (1997),  369–383  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 113:3 (1997), 1508–1519  isi
32. V. V. Vedenyapin, Yu. N. Orlov, “Asymptotics of the spectrum of quantum Hamiltonians”, Dokl. Akad. Nauk, 351:4 (1996),  444–447  mathnet  mathscinet  zmath
33. V. V. Vedenyapin, “Exponent Series and Superposition of Running Waves”, Keldysh Institute preprints, 1995, 117  mathnet
34. V. V. Vedenyapin, O. V. Mingalyov, “Semiboundedness and Asimptotic Behavior of Spectrum of three Quantum Hamiltonians”, Keldysh Institute preprints, 1995, 049  mathnet
35. V. V. Vedenyapin, Yu. N. Orlov, I. P. Pavlotskii, V. M. Suslin, A. S. Shumovsky, “Estimation of Eigenvalues in the Raman-Type Nonlinear Model”, Keldysh Institute preprints, 1995, 041  mathnet
36. V. V. Vedenyapin, O. V. Mingalyov, “Representations of General Commutative Relations. Conservation Laws for Quantum Hamiltonians”, Keldysh Institute preprints, 1995, 030  mathnet
37. Yu. Yu. Arkhipov, V. V. Vedenyapin, “On the classification and stability of steady-state solutions of Vlasov's equation on a torus and in a boundary value problem”, Trudy Mat. Inst. Steklov., 203 (1994),  13–20  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 203 (1995), 11–17
38. V. V. Vedenyapin, I. V. Mingalev, O. V. Mingalev, “On discrete models of the quantum Boltzmann equation”, Mat. Sb., 184:11 (1993),  21–38  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 80:2 (1995), 271–285  isi
39. V. V. Vedenyapin, “Classification of stationary solutions of the Vlasov equation on a torus and a boundary value problem”, Dokl. Akad. Nauk, 323:6 (1992),  1004–1006  mathnet  mathscinet  zmath; Dokl. Math., 45:2 (1992), 459–462
40. V. V. Vedenyapin, “Differential forms in spaces without a norm. A theorem on the uniqueness of Boltzmann's $H$-function”, Uspekhi Mat. Nauk, 43:1(259) (1988),  159–179  mathnet  mathscinet  zmath; Russian Math. Surveys, 43:1 (1988), 193–219
41. V. V. Vedenyapin, “Boundary value problems for a stationary Vlasov equation”, Dokl. Akad. Nauk SSSR, 290:4 (1986),  777–780  mathnet  mathscinet  zmath
42. V. V. Vedenyapin, “Differential forms in infinite-dimensional spaces and their use in kinetic equations”, Funktsional. Anal. i Prilozhen., 19:1 (1985),  62–63  mathnet  mathscinet  zmath; Funct. Anal. Appl., 19:1 (1985), 50–52  isi
43. V. V. Vedenyapin, “Anisotropic solutions of a nonlinear Boltzmann equation for Maxwell molecules”, Dokl. Akad. Nauk SSSR, 256:2 (1981),  338–342  mathnet  mathscinet
44. V. V. Vedenyapin, “On the uniqueness of Boltzmann's $H$-function”, Dokl. Akad. Nauk SSSR, 233:5 (1977),  765–768  mathnet  mathscinet  zmath
45. A. V. Bobylev, V. V. Vedenyapin, “On the maximum principle for discrete models of the Boltzmann equation and on the connection between the direct and inverse collision integrals of this equation”, Dokl. Akad. Nauk SSSR, 233:4 (1977),  519–522  mathnet  mathscinet  zmath
46. V. V. Vedenyapin, “On an inequality for convex functions and on an estimate of the collision integral of the Boltzmann equation for a gas of elastic spheres”, Dokl. Akad. Nauk SSSR, 226:5 (1976),  997–1000  mathnet  mathscinet  zmath
47. V. V. Vedenyapin, “On global solvability of the Cauchy problem for some discrete models of Boltzmann's equation”, Dokl. Akad. Nauk SSSR, 215:1 (1974),  21–23  mathnet  mathscinet  zmath

Presentations in Math-Net.Ru
1. Уравнение Власова-Максвелла-Эйнштейна и анализ лямбда-члена
V. V. Vedenyapin
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
April 11, 2019 11:00
2. Кинетические уравнения Больцмана, Власова и Лиувилля: энтропия и метод Гамильтона-Якоби в негамильтоновой ситуации
V. V. Vedenyapin
Differential geometry and applications
October 29, 2018 16:45
3. Уравнения Власова, геодезические, энтропия по Больцману и Пуанкаре и метод Гамильтона-Якоби
V. V. Vedenyapin

October 22, 2018
4. Кинетические уравнения Больцмана, Власова и Лиувилля: энтропия и метод Гамильтона-Якоби
V. V. Vedenyapin, V. V. Kazantseva
Infinite dimensional analysis and mathematical physics
November 20, 2017 18:30
5. Экстремали Больцмана и эргодическая проблема по Пуанкаре и Гиббсу
S. Z. Adzhiev, V. V. Vedenyapin
All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov
November 13, 2017 17:05
6. $H$-теорема по Больцману и Пуанкере
V. V. Vedenyapin
Knots and Representation Theory
September 19, 2017 17:00
7. Экстремали Больцмана, метод Гамильтона-Якоби в негамильтоновой ситуации и матрица плотности в квантовой механике
V. V. Vedenyapin, V. V. Kazantseva
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
May 4, 2017 11:00
8. Гидродинамическая подстановка в уравнениях Власова и Лиувилля
V. V. Vedenyapin
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
July 27, 2016 14:00
9. Vlasov and Lioville equations and hydrodynamic-type equations
V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin
International Conference on Mathematical Control Theory and Mechanics
July 4, 2015 09:40
10. Forward and reverse fotoforez, Crookes radiometer and reactive power
Ya. G. Batishcheva, V. V. Vedenyapin, I. V. Melikhov
International Conference on Differential Equations and Dynamical Systems
July 5, 2014 09:45
11. Эргодическая теория и экстремали Больцмана
V. V. Vedenyapin, S. Z. Adzhiev, M. A. Negmatov
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
March 19, 2014 16:00
12. Entropy by Boltzmann & Poincaré and Mark Kac's Model
V. V. Vedenyapin, S. Z. Adzhiev
Dobrushin Mathematics Laboratory Seminar
November 19, 2013 16:00
13. Энтропия в кинетической и эргодической теориях
V. V. Vedenyapin
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
July 17, 2013 14:00
14. Инварианты и дискретизация кинетических уравнений Больцмана и Лиувилля
S. Z. Adzhiev, V. V. Vedenyapin
Seminar by Department of Differential Equation, Steklov Mathematical Institute of RAS
May 29, 2013 12:00
15. О движении твердого тела в сопротивляющейся среде
V. V. Vedenyapin
Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS
January 16, 2013 14:00
16. Перспективы неравновесной статистической физики и социологии: вывод уравнений типа Больцмана и нелинейных марковских процессов
V. V. Vedenyapin
Problems in Stochastic Analysis
January 10, 2013 12:00   
17. Н-теорема для обобщений уравнений химической кинетики и уравнения Лиувилля
V. V. Vedenyapin
Problems in Stochastic Analysis
November 3, 2012 12:00   
18. On Liouville and Vlasov equations, and its hydrodynamic consequences
V. V. Vedenyapin, M. A. Negmatov
International Workshop «Geometric Structures in Integrable Systems»
October 30, 2012 18:10   
19. Entropy for generalised quantum kinetic and Liouville equations
S. Z. Adzhiev, V. V. Vedenyapin
International Workshop «Geometric Structures in Integrable Systems»
October 30, 2012 15:50   
20. О движении твердого тела в реагирующей среде и явление фотофореза
V. V. Vedenyapin, Ya. G. Batishcheva, I. V. Melikhov
P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics
April 23, 2012 18:30
21. Инварианты и дискретизация кинетических уравнений Больцмана и Лиувилля и круговая модель М.Каца
S. Z. Adzhiev, V. V. Vedenyapin

April 23, 2012
22. Vlasov–Maxwell and Vlasov–Poisson equations and irreversibility problem
V. V. Vedenyapin, M. A. Negmatov
International Conference "Irreversibility Problem in Classical and Quantum Dynamical Systems"
December 8, 2011 17:20
23. Принцип Больцмана, сопряжённые уравнения и временные средние
V. V. Vedenyapin
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
March 13, 2008 11:00

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