Skip to main content
SpringerLink
Log in

Some examples of NSA methods in kinetic theory

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

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

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. Albeverio, S., Fenstad, J.E., Høegh-Krohn, R., Lindstrøm, T., Nonstandard methods in stochastic analysis and mathematical physics, New York, Acad. Press, 1986.

    MATH  Google Scholar 

  2. Hurd, A., Loeb, P., An introduction to nonstandard real analysis, New York, Acad. Press, 1985.

    MATH  Google Scholar 

  3. Keisler, J., The hyperreal line, Synthese, to appear.

    Google Scholar 

  4. Lindstrøm, T., An invitation to nonstandard analysis, in Nonstandard analysis and its applications, ed. N. Cutland, U.K., Cambridge Univ. Press, 1988.

    Google Scholar 

References

  1. Cutland, N., Internal controls and relaxed controls, J. London Math. Soc. 27, 130–140 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  2. Illner, R. and Reed, M.C., The decay of solutions to the Carleman model, Math. Meth. Appl. Sci. 3, 121–127 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  3. Kolodner, I.I., On the Carleman model, Ann. Mat. pura appl. 63, Series 4, 11–32 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  4. Wick, J., Some remarks on the Carleman model, Tagungsbericht 47/1982, Oberwolfach, also in Math. Meth. Appl. Sci. 6, 515 (1984).

    Article  MathSciNet  Google Scholar 

References

  1. Arkeryd, L. and Illner, R., The Broadwell model in a box, preprint 1992.

    Google Scholar 

  2. Beale, J.T., Large time behaviour of a Broadwell model of a discrete velocity gas, Comm. Math. Phys. 102, 217–235 (1985).

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Arkeryd, L., On the Enskog equation in two space variables, Transp. Theory, Stat. Phys. 15, 673–691 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  2. Arkeryd, L., The nonlinear Boltzmann equation far from equilibrium, in Nonstandard analysis and its applications, ed. N. Cutland, U.K., Cambridge Univ. Press, 1988.

    Google Scholar 

  3. Arkeryd, L., On the strong L1 trend to equilibrium for the Boltzmann equation, Stud. Appl. Math. to appear.

    Google Scholar 

  4. Desvillettes, L., Convergence to equilibrium in large time for Boltzmann and B.G.K. equations, Arch. Rat. Mech. Anal. 110, 73–91 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  5. DiPerna, R. and Lions, P.L., Global solutions of Boltzmann's equation and the entropy inequality, Arch. Rat. Mech. Anal.114, 47–55 (1991).

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Arkeryd, L., Cercignani, C. and Illner, R., Measure solution of the steady Boltzmann equation in a slab, Comm. Math. Phys. 142, 285–296 (1991).

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Arkeryd, L., Existence theorems for certain kinetic equations and large data, Arch. Rat. Mech. Anal. 103, 139–149 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  2. Arkeryd, L., Caprino S., Pulvirenti M., In preparation.

    Google Scholar 

  3. Frisch, H.L., Lebowitz, J.L., Model of nonequilibrium ensemble, Phys. Rev. 107, 917–923 (1957).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. L. Arkeryd
    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

Arkeryd, L. (1993). Some examples of NSA methods in kinetic theory. 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/BFb0090928

Download citation

  • DOI: https://doi.org/10.1007/BFb0090928

  • 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