<?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%">EXISTENCE, UNIQUENESS AND QUENCHING OF THE SOLUTION FOR A NONLOCAL DEGENERATE SEMILINEAR PARABOLIC PROBLEM</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%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/551-560-Chan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">9</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 a and T be positive constants, D = (0, a), D¯ = [0, a], Ω = D × (0, T], and Lu = x qut − uxx, where q is a nonnegative number. This article studies the following problem, Lu(x,t) = Zx 0 k(y)f(u(y,t))dy in Ω, where k is a positive function on D¯, f &amp;gt; 0, f 0≥ 0, f 00≥ 0, and limu→1− f(u) = ∞, subject to the initial condition u(x, 0) = 0 on D¯, and the boundary conditions u(0,t) = 0 = u(a,t) for 0 &amp;lt; t ≤ T. Existence of a unique solution, the critical length, and the quenching behavior of the solution are studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">551</style></section></record></records></xml>