Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition
Zhengce Zhang, Yanyan Li · Applied Mathematics · 2011
We study the porous medium equation ut=(um). 0＜x＜∞, t＞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.