具有奇异淬火项的多维慢扩散方程的点态梯度估计
Pointwise gradient estimates in multi-dimensional slow diffusion equations with a singular quenching term
摘要：
本文考虑一个带有奇异淬火项的慢扩散方程，推广了B. Kawohl和R. Kersner对于一维情形。除了存在一个非常弱解，我们证明了一些逐点梯度估计，主要是当吸收占主导地位的扩散。特别地，证明了一种新的泛梯度估计。几个定性性质（如有限时间淬火现象和有限的传播速度）和研究的柯西问题也被认为是。
英文摘要：
We consider a slow diffusion equation with a singular quenching term, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution, we prove some pointwise gradient estimates, mainly when the absorption dominates over the diffusion. In particular, a new kind of universal gradient estimate is proved. Several qualitative properties (such as the finite time quenching phenomena and the finite speed of propagation) and the study of the Cauchy problem are also considered.
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