Skip to main content
SpringerLink
Log in

Nonequilibrium problems in many-particle systems. An introduction

  • Chapter
  • First Online:
Nonequilibrium Problems in Many-Particle Systems

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1551))

  • 507 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Cercignani, The Boltzmann equation and its applications, Springer, New York (1988).

    Book  MATH  Google Scholar 

  2. J. C. Maxwell, Philosophical Transactions of the Royal Society of London 157, 49–88 (1867).

    Article  Google Scholar 

  3. L. Boltzmann, Sitzungsberichte Akad. Wiss., Vienna, part II, 66, 275–370 (1872).

    Google Scholar 

  4. D. Hilbert, Mathematische Annalen 72, 562–577 (1912).

    Article  MathSciNet  Google Scholar 

  5. S. Chapman, Proceedings of the Royal Society (London) A93, 1–20 (1916/17).

    Article  Google Scholar 

  6. D. Enskog, Kinetische Theorie der Vorgänge in mässig verdünnten Gasen, I. Allgemeiner Teil, Almqvist & Wiksell, Uppsala (1917).

    MATH  Google Scholar 

  7. T. Carleman, Acta Mathematica 60, 91–146 (1933).

    Article  MathSciNet  Google Scholar 

  8. T. Carleman, Problèmes Mathématiques dans la Théorie Cinétique des Gaz, Almqvist & Wiksell, Uppsala (1957).

    MATH  Google Scholar 

  9. H. Grad, Comm. Pure Appl. Math. 2, 331–407 (1949).

    Article  MathSciNet  Google Scholar 

  10. C. Truesdell, Jour. Rat. Mech. Anal. 5, 55–128 (1956).

    MathSciNet  Google Scholar 

  11. V. S. Galkin PMM (in Russian) 20, 445–446 (1955).

    MathSciNet  Google Scholar 

  12. V. S. Galkin, PMM 22, 532–536 (1958).

    MathSciNet  Google Scholar 

  13. D. Morgenstern, Proceedings of the National Academy of Sciences (U.S.A.) 40, 719–721 (1954).

    Article  MathSciNet  Google Scholar 

  14. L. Arkeryd, Arch. Rat. Mech. Anal. 45, 1–16 (1972).

    MathSciNet  Google Scholar 

  15. L. Arkeryd, Arch. Rat. Mech. Anal. 45, 17–34 (1972).

    MathSciNet  Google Scholar 

  16. C. Cercignani, Mathematical Methods in Kinetic Theory, Plenum Press, New York (1969).

    Book  MATH  Google Scholar 

  17. H. Grad, Proceedings of the American Mathematical Society Symposia on Applied Mathematics 17, 154–183 (1965).

    Article  MathSciNet  Google Scholar 

  18. S. Ukai, Proceedings of the Japan Academy 50, 179–184 (1974).

    Article  MathSciNet  Google Scholar 

  19. T. Nishida and K. Imai, Publications of the Research Institute for Mathematical Sciences, Kyoto University 12, 229–239 (1977).

    Article  MathSciNet  Google Scholar 

  20. Y. Shizuta and K. Asano, Proceedings of the Japan Academy 53, 3–5 (1974).

    Article  MathSciNet  Google Scholar 

  21. C. Cercignani, Trans. Theory Stat. Phys., 211–225 (1972).

    Google Scholar 

  22. O. Lanford, III, in Dynamical Systems, Theory and Applications, J. Moser, Ed., LNP 35, 1, Springer, Berlin (1975).

    Google Scholar 

  23. R. Illner and M. Pulvirenti, Commun. Math. Phys. 105, 189–203 (1986).

    Article  MathSciNet  Google Scholar 

  24. R. Illner and M. Pulvirenti, Comm. Math. Phys. 121, 143–146 (1989).

    Article  MathSciNet  Google Scholar 

  25. R. Illner and M. Shinbrot, Comm. Math. Phys., 95, 217–226 (1984).

    Article  MathSciNet  Google Scholar 

  26. R. Di Perna and P. L. Lions, Ann. of Math. 130, 321–366 (1989).

    Article  MathSciNet  Google Scholar 

  27. C. Cercignani, J. Stat. Phys. 58, 817–824 (1990).

    Article  MathSciNet  Google Scholar 

  28. L. Arkeryd and C. Cercignani, Rend. Mat. Acc. Lincei s. 9, 1, 139–149 (1990).

    MathSciNet  Google Scholar 

  29. R. Caflisch, Comm. Pure Appl. Math. 33, 651–666 (1980).

    Article  MathSciNet  Google Scholar 

  30. M. Lachowicz, Math. Meth. in Appl. Sic. 9, 342–366 (1987).

    Article  MathSciNet  Google Scholar 

  31. T. Nishida, Comm. Math. Phys. 112, 119–148 (1978).

    Article  MathSciNet  Google Scholar 

  32. S. Ukai and K. Asano, Hokkaido Math. J. 12, 303–324 (1983)

    MathSciNet  Google Scholar 

  33. W. Braun, K. Hepp, Comm. Math. Phys. 56, 101–120 (1977).

    Article  MathSciNet  Google Scholar 

  34. R. L. Dobrushin, Sov. J. Funct. Anal. 13, 115–119 (1979)

    Article  MathSciNet  Google Scholar 

  35. H. Neunzert, in Kinetic Theories and the Boltzmann Equation, C. Cercignani, ed., 60–110, LNP 1048, 207, Springer, Berlin (1984).

    Chapter  Google Scholar 

  36. K. Oelschläger, Arch. Rat. Mech. Anal. (to appear, 1993).

    Google Scholar 

  37. S. Caprino, R. Esposito, R. Marra and M. Pulvirenti, Comm. PDE (to appear, 1993).

    Google Scholar 

  38. A. De Masi, R. Esposito and J. L. Lebowitz, Comm. Pure Appl. Math. 42, 1189–1214 (1989).

    Article  MathSciNet  Google Scholar 

  39. C. Bardos, F. Golse, D. Levermore, J. Stat. Phys. 63, 323–344 (1991).

    Article  MathSciNet  Google Scholar 

  40. C. Bardos, F. Golse, D. Levermore, Fluid dynamical limits of kinetic equations II. Convergence proof for the Boltzmann equation. Preprint.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    C. Cercignani

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy

    M. Pulvirenti

Authors
  1. C. Cercignani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Pulvirenti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Carlo Cercignani Mario Pulvirenti

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this chapter

Cite this chapter

Cercignani, C., Pulvirenti, M. (1993). Nonequilibrium problems in many-particle systems. An introduction. In: Cercignani, C., Pulvirenti, M. (eds) Nonequilibrium Problems in Many-Particle Systems. Lecture Notes in Mathematics, vol 1551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090927

Download citation

  • DOI: https://doi.org/10.1007/BFb0090927

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56945-9

  • Online ISBN: 978-3-540-47832-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation