Author(s)

Zhengce Zhang, Yanyan Li

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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.

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

Z. 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.