Meccanica

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

Functional methods in three-dimensional neutron transport theory

  • Giorgio Busoni
  • Giovanni Frosali
  • Luigi Mangiarotti
Article

Summary

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.

Keywords

Mechanical Engineer Banach Space Civil Engineer Spatial Variable Physical Parameter 

Sommario

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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References

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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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