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

Zhengce Zhang, Yanyan Li

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DOI: 10.4236/am.2011.29157                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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