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.
Biography
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).
V. V. Vedenyapin, “On derivation of Vlasov–Maxwell–Einstein equations from the principle of least action, the Hamilton–Jacobi method, and the Milne–Mccrea model”, Dokl. RAN. Math. Inf. Proc. Upr., 515 (2024), 60–65; Dokl. Math., 109:1 (2024), 47–51
2.
V. V. Vedenyapin, V. M. Aushev, A. O. Gladkov, Yu. A. Izmailova, A. A. Rebrova, “Mathematical theory of the accelerated expansion of the Universe based on the principle of least action and the Friedman and Milne-McCrea model”, Keldysh Institute preprints, 2024, 003, 28 pp.
3.
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems”, TMF, 218:2 (2024), 258–279; Theoret. and Math. Phys., 218:2 (2024), 222–240
2023
4.
V. V. Vedenyapin, A. A. Bay, A. G. Petrov, “On derivation of equations of gravitation from the principle of least action, relativistic Milne-Mccree solutions and Lagrange points”, Dokl. RAN. Math. Inf. Proc. Upr., 514:1 (2023), 69–73; Dokl. Math., 108:3 (2023), 481–485
5.
V. V. Vedenyapin, D. A. Kogtenev, “On Derivation and Properties of Vlasov-type equations”, Keldysh Institute preprints, 2023, 020, 18 pp.
2022
6.
V. G. Romanov, V. V. Vedenyapin, V. V. Vasin, O. A. Kovyrkina, V. V. Ostapenko, V. F. Tishkin, I. V. Astashova, D. A. Lashin, A. V. Filinovskii, “Erratum to: Several Articles in Doklady Mathematics”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 404–405; Dokl. Math., 106:2 (2022), 404–405
7.
V. V. Vedenyapin, “On derivation of equations of electrodynamics and gravitation from the principle of least action, the Hamilton–Jacobi method, and cosmological solutions”, Dokl. RAN. Math. Inf. Proc. Upr., 504 (2022), 51–55; Dokl. Math., 105:3 (2022), 178–182
V. V. Vedenyapin, V. I. Parenkina, A. G. Petrov, Zhang Haochen, “Vlasov-Einstein equation and Lagrange points”, Keldysh Institute preprints, 2022, 023, 23 pp.
V. V. Vedenyapin, V. I. Parenkina, S. R. Svirshchevskii, “Derivation of the equations of electrodynamics and gravity from the principle of least action”, Zh. Vychisl. Mat. Mat. Fiz., 62:6 (2022), 1016–1029; Comput. Math. Math. Phys., 62:6 (2022), 983–995
S. Z. Adzhiev, V. V. Vedenyapin, I. V. Melikhov, “Kinetic aggregation models leading to morphological memory of formed structures”, Zh. Vychisl. Mat. Mat. Fiz., 62:2 (2022), 255–269; Comput. Math. Math. Phys., 62:2 (2022), 254–268
2020
11.
S. Z. Adzhiev, Ya. G. Batishcheva, V. V. Vedenyapin, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, M. A. Negmatov, Yu. N. Orlov, N. N. Fimin, V. M. Chechetkin, “S.K. Godunov and kinetic theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences”, Zh. Vychisl. Mat. Mat. Fiz., 60:4 (2020), 621–625; Comput. Math. Math. Phys., 60:4 (2020), 610–614
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.
15.
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
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Equation of Vlasov–Maxwell–Einstein type and transition to a weakly relativistic approximation”, Zh. Vychisl. Mat. Mat. Fiz., 59:11 (2019), 1883–1898; Comput. Math. Math. Phys., 59:11 (2019), 1816–1831
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
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.
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; Comput. Math. Math. Phys., 58:9 (2018), 1462–1476
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; Izv. Math., 81:3 (2017), 505–541
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; Comput. Math. Math. Phys., 57:12 (2017), 2017–2029
V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Uspekhi Mat. Nauk, 69:6(420) (2014), 45–80; Russian Math. Surveys, 69:6 (2014), 995–1029
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; Journal of Mathematical Sciences, 202:5 (2014), 769–782
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; Theoret. and Math. Phys., 170:3 (2012), 394–405
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; Comput. Math. Math. Phys., 51:11 (2011), 1942–1952
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; Comput. Math. Math. Phys., 47:6 (2007), 998–1006
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; Comput. Math. Math. Phys., 44:3 (2004), 523–528
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
V. V. Vedenyapin, S. A. Amosov, “Discrete models of the Boltzmann equation for mixtures”, Differ. Uravn., 36:7 (2000), 925–929; Differ. Equ., 36:7 (2000), 1027–1032
V. V. Vedenyapin, “Discrete Velocity Models for Mixtures”, Keldysh Institute preprints, 1999, 017
38.
V. V. Vedenyapin, S. A. Amosov, L. Toscano, “Invariants for Hamiltonians and kinetic equations”, Uspekhi Mat. Nauk, 54:5(329) (1999), 153–154; Russian Math. Surveys, 54:5 (1999), 1056–1057
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; Theoret. and Math. Phys., 121:2 (1999), 1516–1523
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
S. A. Amossov, V. V. Vedenyapin, “On the Vlasov-Einstein Equation and Quantization of Vlasov Equation”, Keldysh Institute preprints, 1997, 013
42.
V. V. Vedenyapin, O. V. Mingalev, I. V. Mingalev, “Representations of general commutation relations”, TMF, 113:3 (1997), 369–383; Theoret. and Math. Phys., 113:3 (1997), 1508–1519
V. V. Vedenyapin, “Exponent Series and Superposition of Running Waves”, Keldysh Institute preprints, 1995, 117
45.
V. V. Vedenyapin, O. V. Mingalyov, “Semiboundedness and Asimptotic Behavior of Spectrum of three Quantum Hamiltonians”, Keldysh Institute preprints, 1995, 049
46.
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
47.
V. V. Vedenyapin, O. V. Mingalyov, “Representations of General Commutative Relations. Conservation Laws for Quantum Hamiltonians”, Keldysh Institute preprints, 1995, 030
1994
48.
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; Proc. Steklov Inst. Math., 203 (1995), 11–17
V. V. Vedenyapin, I. V. Mingalev, O. V. Mingalev, “On discrete models of the quantum Boltzmann equation”, Mat. Sb., 184:11 (1993), 21–38; Russian Acad. Sci. Sb. Math., 80:2 (1995), 271–285
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; Dokl. Math., 45:2 (1992), 459–462
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; Russian Math. Surveys, 43:1 (1988), 193–219
V. V. Vedenyapin, “Differential forms in infinite-dimensional spaces and their use in kinetic equations”, Funktsional. Anal. i Prilozhen., 19:1 (1985), 62–63; Funct. Anal. Appl., 19:1 (1985), 50–52
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
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
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
Уравнение Власова-Эйнштейна и точки Лагранжа V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, A. G. Petrov Hamiltonian systems and statistical mechanics November 28, 2022 16:30
4.
Уравнение Власова-Эйнштейна и точки Лагранжа V. V. Vedenyapin Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS (Novikov Seminar) October 26, 2022 18:30
5.
Об уравнениях типа Власова V. V. Vedenyapin Principle Seminar of the Department of Probability Theory, Moscow State University April 13, 2022 16:45
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 (Novikov Seminar) July 27, 2016 14:00
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
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 (Novikov Seminar) July 17, 2013 14:00
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 (Novikov Seminar) January 16, 2013 14:00