中文摘要：

分数次渗流方程对统计力学和热控制的研究具有重要意义．本文作者对一类分数次渗流方程的柯西问题进行了研究．文章先给出该问题弱解和弱能量解的定义，然后证明了弱解的存在性和弱能量解的唯一性．

英文摘要：

Fractional filtration equation is very important in the studies of statistical mechanics and heat control. In this paper, the authors consider the Cauchy problem of fractional filtration equation. First, the definitions of the weak solution and the weak energy solution to the Cauchy problem are given, then the existence of the weak solution and the uniqueness of the weak energy solution to the problem are shown.