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

Abstract

We study the porous medium equation*u*_{t}=(*u*^{m}). 0＜*x*＜∞, *t*＞0 with a singular boundary condition (*u*^{m}) (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.

We study the porous medium equation

Cite this paper

nullZ. Zhang and Y. Li, "Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition,"*Applied Mathematics*, Vol. 2 No. 9, 2011, pp. 1134-1139. doi: 10.4236/am.2011.29157.

nullZ. Zhang and Y. Li, "Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition,"

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