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Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition
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Applied Mathematics·Volume 02 (2011)·Pages 1134–1139·Published 29 September 2011·DOI10.4236/am.2011.29157
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Abstract
We study the porous medium equation <i>u<sub>t</sub></i>=(<i>u<sup>m</sup></i>). 0＜<i>x</i>＜∞, <i>t</i>＞0 with a singular boundary condition (<i>u<sup>m</sup></i>) (0,<i>t</i>)=<i>u<sup>-β</i></sup>(0,<i>t</i>). We prove finite time quenching for the solution at the boundary <i>χ</i>=0. We also establish the quenching rate and asymptotic behavior on the quenching point.
KeywordsPorous Medium EquationQuenching ProfileQuenching RateSingular Boundary Condition
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