【摘要】 该文讨论如下空间非均匀的Boltzmann方程(?)f/(?)t+ξ·▽xf(t,x,ξ)=Q(f,f).在角截断的硬位势情况下,对初值接近行波Maxwell分布时,作者利用一种新的迭代方法,证明了该方程存在一个非负的永久型解．因此在空间区域无界的情形下,该文对Villani的猜测给出了否定的回答．更多还原

【Abstract】 In this paper, the authors discuss the following spatially inhomogeneous Boltzmann equation (?)f/(?)t+ξ·▽xf(t,x,ξ)=Q(f,f). By means of a new iteration method, the existence of a positive eternal solution with initial data close to a travelling Maxwellian is proved in the case of hard potentials with angular cutoff. Hence, the authors give a negative answer to the conjecture of Villanil in the case of unbounded space domain.更多还原