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
219-222
,共4页
Boltzmann equation%quantum effects%existence%uniqueness%entropy identity%spatial decay
A previous study[1] is continued by investigating the Boltzmann equation for particles with quantum effects (BQE). First, the corresponding entropy identity is proved, then if the initial data f(x,v,0) satisfies 0≤f(x,v,0)≤CΦ(x,v,0) for a constant 0＜C＜∞ and function Φ(x,v,t), we prove the existence and uniqueness of spatial decay solutions of the BQE within a given function space B(Φ) using fixed point theory. Moreover, if there is a continuous function F(x,v) which belongs to a function set, then there exists a mild solution f(x,v,t) of the BQE such that f∞(x,v)= limt→∞f(x+vt,v,t)=F(x,v).
