We study the one-dimensional free streaming operator in a slab domain with general boundary conditions described by a linear positive operator Λ. Under the assumptions that Λ-1 exists and is positive and the free streaming operator TΛ is resolvent positive, we prove that TΛ is the infinitesimal generator of a positive strongly continuous semigroup, which is contractive if ∥ Λ ∥ ≤ 1 and quasi-bounded if ∥ Λ A∥ > 1 and ∥ Λ-1 ∥ ≤ 1. We give also the mathematical definition of dissipative, conservative and multiplying boundary walls in terms of Λ, and we show how these properties of the boundary walls can affect the type of the semigroup generated by TΛ.

Semigroup generation properties of the streaming operator in dependence of the boundary conditions / G. BORGIOLI; S. TOTARO. - In: TRANSPORT THEORY AND STATISTICAL PHYSICS. - ISSN 0041-1450. - STAMPA. - 25:(1996), pp. 491-502. [10.1080/00411459608220716]

Semigroup generation properties of the streaming operator in dependence of the boundary conditions

BORGIOLI, GIOVANNI
;
TOTARO, SILVIA
1996

Abstract

We study the one-dimensional free streaming operator in a slab domain with general boundary conditions described by a linear positive operator Λ. Under the assumptions that Λ-1 exists and is positive and the free streaming operator TΛ is resolvent positive, we prove that TΛ is the infinitesimal generator of a positive strongly continuous semigroup, which is contractive if ∥ Λ ∥ ≤ 1 and quasi-bounded if ∥ Λ A∥ > 1 and ∥ Λ-1 ∥ ≤ 1. We give also the mathematical definition of dissipative, conservative and multiplying boundary walls in terms of Λ, and we show how these properties of the boundary walls can affect the type of the semigroup generated by TΛ.
1996
25
491
502
G. BORGIOLI; S. TOTARO
File in questo prodotto:
File Dimensione Formato  
Totaro_TTSP1996.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 459.1 kB
Formato Adobe PDF
459.1 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/8171
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? ND
social impact