C. Y. Chan and M. K. Kwong, “Quenching Phenomena for Singular Nonlinear Parabolic Equations,” Nonlinear Analysis, Vol. 12, No. 2, 1998, pp. 1377-1383. doi:10.1016/0362-546X(88)90085-5

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.