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H. A. Levine and G. M. Lieberman, “Quenching of Solutions of Parabolic Equations with Nonlinear Boundary Conditions in Several Dimensions,” Journal für Die Reine und Angewandte Mathematik, Vol. 1983, No. 345, 1983, pp. 23-38.

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.