<?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%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">H. T. LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUENCHING FOR DEGENERATE PARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS</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%">35K20</style></keyword><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/18/02-DSA-CY-2-ChanLiu.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%">12</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 q be a nonnegative real number, and a and T be positive constants. This article studies the following degenerate parabolic problem: x qut − uxx = G(u) in (0, a) × (0, T], where G is a nonnegative function in the form of either f(u(x, t)), or Ra 0 h(x, t) f(u(x, t))dx for some positive, bounded and continuous function h with f &amp;gt; 0, f 0&amp;gt; 0, f 00≥ 0, and limu→1− f(u) = ∞. It is subject to the initial condition, u(x, 0) = 0 on [0, a], and the boundary conditions, u(0, t) = Za 0 M(x)|u (x, t)| p dx, u (a, t) = Za 0 N (x)|u (x, t)| r dx, t &amp;gt; 0, where p and r are constants greater than or equal to 1, and M and N are given nonnegative functions. Existence, uniqueness and criteria for quenching and non-quenching are studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">17</style></section></record></records></xml>