Sommario
Si considerano alcuni tipi di condizioni al contorno per l'operatore di streaming T in teoria della radiazione. Innanzitutto, si studia l'operatore di streaming T in un mezzo finito convesso con condizioni al contorno di riflessione diffusa e con condizioni di tipo misto. In entrambi i casi si prova che T è il generatore di un semigruppo fortemente continuo, sotto l'ipotesi che la superficie del contorno sia sufficientemente regolare. Si indaga poi il caso della riflessione speculare. Costruito il relativo semigruppo di evoluzione con considerazioni fisiche, si dà infine un'esatta descrizione del corrispondente generatore.
Summary
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.
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Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica).
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Busoni, G., Frosali, G. Streaming operators and semigroups. Meccanica 14, 119–128 (1979). https://doi.org/10.1007/BF02128504
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DOI: https://doi.org/10.1007/BF02128504