Doubly Degenerate Parabolic Equation with Time-Dependent Gradient Source and Initial Data Measures

This paper is devoted to the Cauchy problem for a class of doubly degenerate parabolic equation with time-dependent gradient source, where the initial data are Radon measures. Using the delicate a priori estimates, we first establish two local existence results. Furthermore, we show that the existence of solutions is optimal in the class considered here.