<?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%">W. Y. CHAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF THE CLASSICAL SOLUTION FOR DEGENERATE QUASILINEAR PARABOLIC PROBLEMS WITH SLOW DIFFUSIONS</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%">35K55</style></keyword><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/18/06-DSA-CY-6-wyChan.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%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T ≤ ∞, b be a positive number, m be a positive number such that m &amp;gt; 1, and q be a nonnegative number. Existence and uniqueness of a classical solution are studied for the following degenerate quasilinear parabolic problem,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; x&lt;sup&gt;q&lt;/sup&gt;u&lt;sub&gt;t &lt;/sub&gt;= ( u&lt;sup&gt;m&amp;nbsp;&lt;/sup&gt;)&lt;sub&gt;xx &lt;/sub&gt;+ bf( u )&amp;nbsp; in (0, 1) × (0, T),&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;u( x, 0 )= u&lt;sub&gt;0&lt;/sub&gt;( x ) in [0, 1], u (0, t) = 0 = u ( 1, t ) for t ∈ (0, T),&lt;/p&gt;

&lt;p&gt;where u&lt;sub&gt;0&lt;/sub&gt;( x ) is a positive function for 0 &amp;lt; x &amp;lt; 1,&amp;nbsp; u&lt;sub&gt;0&lt;/sub&gt;&lt;sup&gt;m&lt;/sup&gt;( x ) ∈ C&lt;sup&gt;2+α&lt;/sup&gt; ( [0, 1] ) for some α ∈ ( 0, 1 ), u&lt;sub&gt;0&lt;/sub&gt;( 0 ) = u&lt;sub&gt;0&lt;/sub&gt;( 1 ) = 0,&amp;nbsp; and f (u) is a given function such that f (0) ≥ 0 and f′ (u) ≥ 0 for u ≥ 0. Furthermore, a criterion for u to blow up in a finite time is given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">63</style></section></record></records></xml>