δ函数汇随时间变化的抛物型位势的Smoluchowski方程的某些精确结果
Some exact results for the Smoluchowski equation for a parabolic potential with time dependent delta function sink
摘要：
在许多特殊情况下，具有时间依赖的δ函数汇的Smoluchowski方程得到了精确解。在所有其他情况下，这个问题都可以归结为一个积分方程。研究表明，只要知道汇点处的概率分布，就可以导出处处概率分布的解析表达式。这样，问题就从两个变量的偏微分方程简化为一个变量的积分方程。据作者所知，我们是第一个给出具有时间相关汇的抛物势的Smoluchowski方程的精确解析解的人。
英文摘要：
The Smoluchowski equation with a time dependent delta function sink is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation. It is shown that by knowing the probability distribution at the position of sink, one can derive analytical expression for probability distribution everywhere. Thus the problem is reduced from a PDE in two variables to an integral equation of one. As far as the authors knowledge, we are the first one to provide an exact analytical solution of Smoluchowski equation for a parabolic potential with time dependent sink.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
