论文标题
多维缓慢扩散方程中的梯度梯度估计值，具有单数淬灭项
Pointwise gradient estimates in multi-dimensional slow diffusion equations with a singular quenching term
论文作者
论文摘要
我们认为具有奇异淬火项的缓慢扩散方程，扩展了B. Kawohl和R. Kersner于1992年对一维情况进行的数学处理。除了存在非常弱的溶液外，我们还证明了一些点式梯度估计值，主要是当吸收在扩散上占主导地位时。特别是，已证明了一种新型的普遍梯度估计。还考虑了几种定性特性（例如有限的时间淬灭现象和有限的传播速度）和库奇问题的研究。
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.
