中文摘要：

研究了方程ut-div（｜Dum｜p-2Dum）=t^-σu^q的Cauchy问题, 其中m〉0, p〉1。此方程为双非线性抛物方程,根据参数m, p的不同取值,方程主部会发生双重退化或双重奇异性。本文利用先验估计和紧性方法以及对参数m, p作精细划分,得到了测度初值解的最优存在性。

英文摘要：

The Cauchy problem of the equation ut-div（｜Dum｜p-2Dum）=t-σuq,is studied, where m〉0, p〉1. This equation is called doubly nonlinear parabolic equation, since the principal part may be doubly degenerate or doubly singular related to the parameters m, p. By a priori estimates and compactness methods, and fine classifications to parameters m, p, we obtain the optimal existence of solutions of the equation with initial data measures are obtained.