<?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%">T. TREEYAPRASERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE, UNIQUENESS AND QUENCHING FOR A PARABOLIC PROBLEM WITH A MOVING NONLINEAR SOURCE ON A SEMI-INFINITE INTERVAL</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%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K61</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/10-dsa-135-142.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">8</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 v and T be positive numbers, D = (0, ∞), Ω = D × (0, T ], and D¯ be the closure of D. This article studies the first initial-boundary value problem, ut − uxx = δ(x − vt)f (u(x, t)) in Ω, u(x, 0) = 0 on D, ¯ u(0, t) = 0, u(x, t) → 0 as x → ∞ for 0 &amp;lt; t ≤ T, where δ (x) is the Dirac delta function, and f is a given function such that limu→c− f(u) = ∞ for some positive constant c. It is shown that the problem has a unique nonnegative continuous solution u, and u(vt, t) is a strictly increasing function of t; also, if u exists for t ∈ [0, tq) with tq &amp;lt; ∞, then sup {u (x, t) : 0 ≤ x &amp;lt; ∞} reaches c − at tq.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">135</style></section></record></records></xml>