In this article, the authors consider equation ut = div（φ（Γu）A（｜Du｜^2）Du） - （u- I）, where φ is strictly positive and F is a known vector-valued mapping, A ： R＋ → R^＋ is decreasing and A（s） -1/ √s as s → ＋∞. This kind of equation arises naturally from image denoising. For an initial datum I ∈ BVloc ∩ L^∞, the existence of BV solutions to the initial value problem of the equation is obtained.
In this paper, we study a initial value problem of a degenerate parabolic equation coupled with time-delay regularization. The existence of BV solutions to the problem for an initial BV10c data is obtained. Moreover, the existence and uniqueness of spatial-periodic classical solutions to its corresponding regularized problem are also given.
