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.