清华大学学报(英文版)
清華大學學報(英文版)
청화대학학보(영문판)
TSINGHUA SCIENCE AND TECHNOLOGY
2002年
3期
215-218
,共4页
Boltzmann equation%quantum effects%spatial decay solution%long time behavior
The Boltzmann equations for Fermi-Dirac particles and Bose-Einstein particles, both in the absence of external force fields, are combined into a more general form called the Boltzmann equation with quantum effects (BQE). It is assumed that the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤cΦ(x,v,0) for a positive constant c and certain types of control functions Φ(x,v,t). Then within a given function space B(Φ), we prove that f(x+tv,v,t) uniformly converges to f∞(x,v) in a certain norm where f∞(x,v)= limt→∞f(x+tv,v,t) and different initial data determines different long time limits.
