研究了一类含有梯度项的奇异型抛物方程. 在一定条件下, 通过抛物正则化方法及上下解方法, 获得了该问题的古典解, 证明了这个解在边界点处的一阶导数为0. 而且,证明了某些奇异问题古典径向解的存在性.
The initial-boundary value problem for a class of singular parabolic equations is discussed. Under some conditions, classical solutions for the problem by parabolic regularization method and sub-super solution method showing that the first derivatives of solutions are zero on the boundary are obtained. Moreover, the existence of classical radial solutions for some singular parabolic problems is proved.