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We consider a slow diffusion equation with a singular quenching term,extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersnerfor the one-dimensional case. Besides the existence of a very weak solution, weprove some pointwise gradient estimates, mainly when the absorption dominatesover the diffusion. In particular, a new kind of universal gradient estimate isproved. Several qualitative properties (such as the finite time quenchingphenomena and the finite speed of propagation) and the study of the Cauchyproblem are also considered.

Pointwise gradient estimates in multi-dimensional slow diffusion equations with a singular quenching term