The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning the theory of micromachines (MEMS) and nanomachines (NENS).
Il lavoro è suddiviso in due parti. La prima presenta un risultato recente dell'autore riguardante l'esistenza della soluzione dell'equazione di Boltzmann per molecole maxwelliane, senza alcun taglio nel nucleo del termine d'urto, quando la soluzione dipende da una sola variabile spaziale. A differenza del ben noto teorema di Di Perna-Lions, si dimostra che vale anche la conservazione dell'energia. La seconda parte presenta problemi di dinamica dei gas rarefatti, retti dall'equazione di Boltzmann riguardanti la teoria delle micromacchine (MEMS) e nanomacchine (NEMS).
@article{BUMI_2007_8_10B_2_293_0,
author = {Carlo Cercignani},
title = {The Boltzmann Equation: Mathematics and Applications},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {10-A},
year = {2007},
pages = {293-315},
zbl = {1178.82042},
mrnumber = {2339443},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_2_293_0}
}
Cercignani, Carlo. The Boltzmann Equation: Mathematics and Applications. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 293-315. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_2_293_0/
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