, Volume 11, Issue 3, pp 127–132 | Cite as

Functional methods in three-dimensional neutron transport theory

  • Giorgio Busoni
  • Giovanni Frosali
  • Luigi Mangiarotti


In this work, we are concerned with the stationary neutron transport Boltzmann equation (in its integral form) in a parallelepiped. Functional methods allow us to prove that the integral transport operator, which is defined in L2 space, has eigenvalues depending continuously and monotonically on geometrical and physical parameters. We show that the eigenfunctions are continuous with respect to set of the spatial variables and the optical parameters. Finally, we remark that the same results are valid if the study is carried out in the Banach space C.


Mechanical Engineer Banach Space Civil Engineer Spatial Variable Physical Parameter 
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In questo lavoro consideriamo l'equazione stazionaria di Boltzmann (nella forma integrale) per neutroni monoenergetici nel caso di un sistema tridimensionale a forma di parallelepipedo. L'uso di alcuni metodi dell'analisi funzionale ci permette di provare che l'operatore integrale del trasporto, definito nello spazio L2, ha autovalori che dipendono continuamente dai parametri geometrici e fisici. Si prova che le autofunzioni sono continue rispetto all'insieme delle variabili spaziali e dei parametri ottici. Infine, si osserva che gli stessi risultati sono validi se l'operatore del trasporto agisce nello spazio di Banach C.


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  1. [1]
    Premuda F.,Boundedness, continuity, positivity and dominance of the solution of the neutron Boltzmann equation, Meccanica,6, 204, 1971.Google Scholar
  2. [2]
    Premuda F.,Dominant critical eigenfunction and Neumann series convergence for inhomogeneous slabs and spheres in integral neutron transport, Meccanica,8, 89, 1973.Google Scholar
  3. [3]
    Boffi V. C., Premuda F. andSpiga G.,Convergence in the mean of solutions to the neutron integral Boltzmann equation in three-dimensional systems, J. Math. Phys.,14, 346, 1973.Google Scholar
  4. [4]
    Mikhlin S. G.,Mathematical Physics, North-Holland, Amsterdam, 1970.Google Scholar
  5. [5]
    Taylor A. E.,Introduction to Functional Analysis, J. Wiley, N. York, 1958.Google Scholar
  6. [6]
    Riesz F. andSz-Nagy B.,Functional Analysis, F. Ungar, N. York, 1965.Google Scholar
  7. [7]
    Mikhlin S. G.,Integral Equations, Pergamon Press, London, 1957.Google Scholar
  8. [8]
    Lehner J. andWing G. M.,On the spectrum of an msymmetric operator arising in the transport theory of neutrons, Comm. Pure Appl. Math.,8, 217, 1955.Google Scholar
  9. [9]
    Wing G. M.,An introduction to transport theory, J. Wiley, New York, 1962.Google Scholar

Copyright information

© Masson Italia Editori S.p.A 1976

Authors and Affiliations

  • Giorgio Busoni
    • 1
  • Giovanni Frosali
    • 1
  • Luigi Mangiarotti
    • 1
  1. 1.Istituto Matematico “U. DINI”Università di FirenzeFirenzeItaly

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