非弹性Kac模型收敛于平衡点的完全刻划
Complete characterization of convergence to equilibrium for an inelastic Kac model
摘要：
普尔维伦蒂和托斯卡尼提出了一个方程，将麦克斯韦气体的卡茨漫画推广到非弹性粒子。我们表明，概率分布，相对柯西问题的解决方案，弱收敛到一个概率分布当且仅当对称化的初始分布属于标准域的吸引对称稳定的法律，其指数$α$是由所谓的程度的非弹性，$p>0$，粒子：$α=\frac{2}{1+p}$。然后使用此结果：（1）说明所有平稳解的类与所有指标为$α$的对称稳定律的类一致。(2)在没有通常采用的附加条件的情况下，求出一个著名的随机函数方程的解。
英文摘要：
Pulvirenti and Toscani introduced an equation which extends the Kac caricature of a Maxwellian gas to inelastic particles. We show that the probability distribution, solution of the relative Cauchy problem, converges weakly to a probability distribution if and only if the symmetrized initial distribution belongs to the standard domain of attraction of a symmetric stable law, whose index $α$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $α=\frac{2}{1+p}$. This result is then used: (1) To state that the class of all stationary solutions coincides with that of all symmetric stable laws with index $α$. (2) To determine the solution of a well-known stochastic functional equation in the absence of extra-conditions usually adopted.
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