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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 121, Number 2, Pages 307–315
DOI: https://doi.org/10.4213/tmf811
(Mi tmf811)
 

This article is cited in 29 scientific papers (total in 29 papers)

Conservation laws for polynomial Hamiltonians and for discrete models of the Boltzmann equation

V. V. Vedenyapin, Yu. N. Orlov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
References:
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.
Received: 22.12.1998
Revised: 20.05.1999
English version:
Theoretical and Mathematical Physics, 1999, Volume 121, Issue 2, Pages 1516–1523
DOI: https://doi.org/10.1007/BF02557222
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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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:
    1. Russian Math. Surveys, 79:3 (2024), 459–513  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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  crossref
    3. 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  crossref
    4. Oleg Ilyin, “Discrete-velocity Boltzmann model: Regularization and linear stability”, Phys. Rev. E, 105:4 (2022)  crossref
    5. Ilyin O., “Discrete Velocity Boltzmann Model For Quasi-Incompressible Hydrodynamics”, Mathematics, 9:9 (2021), 993  crossref  isi
    6. 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  mathnet  crossref  crossref  isi  elib
    7. 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  crossref
    8. Bernhoff N., “Discrete Velocity Models For Polyatomic Molecules Without Nonphysical Collision Invariants”, J. Stat. Phys., 172:3 (2018), 742–761  crossref  mathscinet  isi  scopus
    9. 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  mathnet  crossref
    10. 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  mathnet  crossref  crossref  isi  elib
    11. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. 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  crossref  mathscinet  isi  scopus  scopus  scopus
    13. 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  crossref  mathscinet  isi  scopus  scopus  scopus
    14. 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  crossref  isi  scopus  scopus  scopus
    15. 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  mathnet  crossref  crossref  isi  elib
    16. Bernhoff N., Vinerean M., “Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants”, J. Stat. Phys., 165:2 (2016), 434–453  crossref  mathscinet  zmath  isi  elib  scopus
    17. V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. 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  crossref  adsnasa  isi  scopus  scopus  scopus
    19. 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  elib
    20. Bobylev, A, “DISCRETE VELOCITY MODELS OF THE BOLTZMANN EQUATION AND CONSERVATION LAWS”, Kinetic and Related Models, 3:1 (2010), 35  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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