Il Nuovo Cimento D

, Volume 7, Issue 3, pp 327–338 | Cite as

An analytical study of space-dependent evolution problems in particle transport theory

  • V. C. Boffi
  • G. Spiga


Space-dependent evolution problems arising in particle transport theory are analytically studied via a systematic application of the Boltzmann equation. Some explicit solutions, that can improve our knowledge of the spatial effects in such a class of problems, are constructed and briefly commented on a physical ground.

PACS. 51.10.

Kinetic and transport theory 

PACS. 66.90

Other topics in nonelectronic transport properties 


Problemi spaziali di evoluzione che si incontrano nella teoria del trasporto di particelle sono studiati analiticamente per mezzo di una sistematica applicazione dell'equazione di Boltzmann. Alcune soluzioni esplicite, che possono migliorare la nostra conoscenza degli effetti spaziali in tale classe di problemi, sono costruite e commentate brevemente su base fisica.


Аналитически, используя уравнение Больцмана, исследуются проблемы пространственной эволюции, зозниакющие в теории переноса частиц. Конструируются некоторые точные решения, которые могут уточнить наше понимание пространственных эффектов в таком классе проблем. Проводится обсуждение этих решений.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. (1).
    W. Greenberg, J. Palewczak andP. F. Zweifel: inNonequilibrium Phenomena: I. The Boltzmann Equation, edited byJ. L. Lebowitz andE. W. Montroll (North-Holland, Amsterdam, 1983).Google Scholar
  2. (2).
    L. Arkeryd:Ark. Rat. Mech. Anal.,86, 85 (1984).MATHMathSciNetCrossRefGoogle Scholar
  3. (3).
    N. Bellomo, R. Illner andG. Toscani:C. R. Acad. Sci. Paris,299, Serie I, 835 (1984).MATHMathSciNetADSGoogle Scholar
  4. (4).
    W. Fiszdon, M. Lachowicz andA. Palczewski: inTrends and Application of Pure Mathematics to Mechanics, edited byP. Ciarlet andM. Roseau, Springer Lecture Note in Physics, No.195 (1984).Google Scholar
  5. (5).
    R. Illner andM. Shinbrot:Commun. Math. Phys.,95, 217 (1984).MATHMathSciNetCrossRefADSGoogle Scholar
  6. (6).
    G. Toscani:Ann. Mat. Pura Appl.,138, 297 (1984).MATHMathSciNetCrossRefGoogle Scholar
  7. (7).
    P. Zweifel: inKinetic Theories and the Boltzmann Equation, edited byC. Cercignani, Springer Lecture Note in Mathematics, No.1048 (1984).Google Scholar
  8. (8).
    N. Bellomo andG. Toscani:J. Math. Phys. (N. Y.),26, 334 (1985).MATHMathSciNetCrossRefADSGoogle Scholar
  9. (9).
    C. Cercignani:Theory and Application of the Boltzmann Equation (Scottish Academic Press, Edinburgh, 1975).MATHGoogle Scholar
  10. (10).
    A. Palczewski:TTSP,14, 1 (1985).MATHMathSciNetADSGoogle Scholar
  11. (11).
    H. G. Kaper, C. G. Lekkerkerker andJ. Hejtmanek:Spectral Methods in Linear Transport Theory (Birkhaüser, Basel, 1982).MATHGoogle Scholar
  12. (12).
    J. H. Ferziger andH. G. Kaper:Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972).Google Scholar
  13. (13).
    M. M. R. Williams:Mathematical Methods in Particle Transport Theory (Butterworths, London, 1971).Google Scholar
  14. (14).
    J. J. Duderstadt andW. R. Martin:Transport Theory (J. Wiley, New York, N. Y., 1979).MATHGoogle Scholar
  15. (15).
    C. V. Boffi andV. Molinari:Nuovo Cimento B,65, 29 (1981).CrossRefADSGoogle Scholar
  16. (16).
    G. Spiga, T. Nonnenmacher andV. C. Boffi:Physica (Utrecht) A,131, 431 (1985).MathSciNetADSGoogle Scholar
  17. (17).
    M. Abramowitz andI. A. Stegun (Editors):Handbook of Mathematical Functions (Dover, New York, N. Y., 1964).MATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1986

Authors and Affiliations

  • V. C. Boffi
    • 1
  • G. Spiga
    • 1
  1. 1.Laboratorio di Ingegneria Nucleare dell'UniversitàBolognaItalia

Personalised recommendations