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H. Kawarada, “On Solutions of Initial Boundary Value Problem for ut = uxx = 1/(1–u),” Publications of the Research Institute for Mathematical Sciences, Vol. 10, 1975, pp. 729-736. doi:10.2977/prims/1195191889

has been cited by the following article:

• TITLE: Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition

  AUTHORS: Zhengce Zhang, Yanyan Li

  KEYWORDS: Porous Medium Equation, Quenching Profile, Quenching Rate, Singular Boundary Condition

  JOURNAL NAME: Applied Mathematics, Vol.2 No.9, September 19, 2011

  ABSTRACT: We study the porous medium equation ut=(um). 0xt＞0 with a singular boundary condition (um) (0,t)=u-β(0,t). We prove finite time quenching for the solution at the boundary χ=0. We also establish the quenching rate and asymptotic behavior on the quenching point.