We consider some types of boundary conditions for the streaming operator T in the radiation theory. First, we study the streaming operator in a finite convex body with diffuse reflection boundary conditions and with mixed type boundary conditions. In both cases, we prove that T is the generator of a strongly continuous semigroup, by assuming a suitable smoothness of a surface of the boundary. We also investigate the specular reflection boundary conditions. In this case, physical considerations suggest the form of the semigroup leading the evolution of the system. Finally, a complete description of the corresponding generator is given.
Streaming operators and semigroups / GIORGIO BUSONI; GIOVANNI FROSALI. - In: MECCANICA. - ISSN 0025-6455. - STAMPA. - 14:(1979), pp. 119-128. [10.1007/BF02128504]
Streaming operators and semigroups
BUSONI, GIORGIO;FROSALI, GIOVANNI
1979
Abstract
We consider some types of boundary conditions for the streaming operator T in the radiation theory. First, we study the streaming operator in a finite convex body with diffuse reflection boundary conditions and with mixed type boundary conditions. In both cases, we prove that T is the generator of a strongly continuous semigroup, by assuming a suitable smoothness of a surface of the boundary. We also investigate the specular reflection boundary conditions. In this case, physical considerations suggest the form of the semigroup leading the evolution of the system. Finally, a complete description of the corresponding generator is given.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.