Abstract:
Conservation laws that are linear with respect to the number of particles are constructed for classical and quantum Hamiltonians. A class of relaxation models generalizing discrete models of the Boltzmann equation are also considered. Conservation laws are written for these models in the same form as for the Hamiltonians.
Citation:
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
\Bibitem{VedOrl99}
\by V.~V.~Vedenyapin, Yu.~N.~Orlov
\paper Conservation laws for polynomial Hamiltonians and for discrete models of the Boltzmann equation
\jour TMF
\yr 1999
\vol 121
\issue 2
\pages 307--315
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\crossref{https://doi.org/10.4213/tmf811}
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\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 121
\issue 2
\pages 1516--1523
\crossref{https://doi.org/10.1007/BF02557222}
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Linking options:
https://www.mathnet.ru/eng/tmf811
https://doi.org/10.4213/tmf811
https://www.mathnet.ru/eng/tmf/v121/i2/p307
This publication is cited in the following 29 articles:
Russian Math. Surveys, 79:3 (2024), 459–513
O. V. Ilyin, “On Accuracy of the Lattice Boltzmann Equations of Low and High Orders as Applied to Slow Isothermal Microflows”, Comput. Math. and Math. Phys., 64:9 (2024), 2131
V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Boltzmann and Poincaré Entropy, Boltzmann Extremals, and Hamilton–Jacobi Method for Non-Hamiltonian Situation”, J Math Sci, 260:4 (2022), 434
Oleg Ilyin, “Discrete-velocity Boltzmann model: Regularization and linear stability”, Phys. Rev. E, 105:4 (2022)
Ilyin O., “Discrete Velocity Boltzmann Model For Quasi-Incompressible Hydrodynamics”, Mathematics, 9:9 (2021), 993
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”, Comput. Math. Math. Phys., 60:4 (2020), 610–614
Sergey Adzhiev, Janina Batishcheva, Igor Melikhov, Victor Vedenyapin, “Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem”, Physics, 1:2 (2019), 229
Bernhoff N., “Discrete Velocity Models For Polyatomic Molecules Without Nonphysical Collision Invariants”, J. Stat. Phys., 172:3 (2018), 742–761
V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Entropiya po Boltsmanu i Puankare, ekstremali Boltsmana i metod Gamiltona–Yakobi v negamiltonovoi situatsii”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 37–59
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”, Comput. Math. Math. Phys., 58:9 (2018), 1462–1476
A. I. Aptekarev, M. A. Lapik, Yu. N. Orlov, “Asymptotic behavior of the spectrum of combination scattering at Stokes phonons”, Theoret. and Math. Phys., 193:1 (2017), 1480–1497
Adzhiev S.Z. Melikhov I.V. Vedenyapin V.V., “The H-Theorem For the Physico-Chemical Kinetic Equations With Explicit Time Discretization”, Physica A, 481 (2017), 60–69
Adzhiev S.Z. Melikhov I.V. Vedenyapin V.V., “The H-Theorem For the Physico-Chemical Kinetic Equations With Discrete Time and For Their Generalizations”, Physica A, 480 (2017), 39–50
Adzhiev S. Melikhov I. Vedenyapin V., “The H-Theorem For the Chemical Kinetic Equations With Discrete Time and For Their Generalizations”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012001
S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Comput. Math. Math. Phys., 57:12 (2017), 2017–2029
Bernhoff N., Vinerean M., “Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants”, J. Stat. Phys., 165:2 (2016), 434–453
V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029
Bobylev A.V., Vinerean M.C., “Symmetric Extensions of Normal Discrete Velocity Models”, 28th International Symposium on Rarefied Gas Dynamics 2012, Vols. 1 and 2, AIP Conference Proceedings, 1501, eds. Mareschal M., Santos A., Amer Inst Physics, 2012, 254–261
Gasnikov A.V., Gasnikova E.V., Fedko O.S., “O vozmozhnoi dinamike v mode- li ranzhirovaniya web-stranits pagerank i modernizirovannoi modeli rascheta matritsy korrespondentsii”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 4:2-14 (2012), 101–120
On possible dynamics in google's pagerank and a new model for a ocorrespondence matrix
Bobylev, A, “DISCRETE VELOCITY MODELS OF THE BOLTZMANN EQUATION AND CONSERVATION LAWS”, Kinetic and Related Models, 3:1 (2010), 35