<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PHILIP W. SCHAEFER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BLOW-UP PHENOMENA IN SOME POROUS MEDIUM PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword><keyword><style  face="normal" font="default" size="100%">35K65</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/08-DSA-CY-8-Schaefer.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider a Dirichlet type initial-boundary value problem for the porous medium equation with a power function reaction term. We determine a condition on the initial data which ensures blow-up of the solution in finite time and an upper bound for the blow-up time. We also discuss when blow-up does not occur and a more general initial-boundary value problem where blow-up does occur.&lt;/p&gt;
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