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

2020/01/28 by Nguyen Anh Dao, Dao, Nguyen Anh, Jesús Ildefonso Díaz Díaz +3
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2001.10193

Abstract

We consider a slow diffusion equation with a singular quenching term,\nextending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner\nfor the one-dimensional case. Besides the existence of a very weak solution, we\nprove some pointwise gradient estimates, mainly when the absorption dominates\nover the diffusion. In particular, a new kind of universal gradient estimate is\nproved. Several qualitative properties (such as the finite time quenching\nphenomena and the finite speed of propagation) and the study of the Cauchy\nproblem are also considered.\n

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