<?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%">Rebiai, Salah-Eddine</style></author><author><style face="normal" font="default" size="100%">Sidi-Ali, Fatima Zohra</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Uniform exponential stability of the transmission wave equation with a delay term in the boundary feedback</style></title><secondary-title><style face="normal" font="default" size="100%">IMA Journal of Mathematical Control and InformationIMA Journal of Mathematical Control and Information</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">33</style></volume><pages><style face="normal" font="default" size="100%">1 - 20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We consider a system of transmission of the wave equation with Neumann feedback control that contains a delay term and acts on the exterior boundary. First, we prove under some assumptions that the closed-loop system generates a C 0 -semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. To establish this result, we introduce a suitable energy function and use multiplier method together with an estimate taken from Lasiecka &amp;amp; Triggiani (1992, Appl. Math. Optim., 25, 189–244.) (Lemma 7.2) and compactness-uniqueness argument.</style></abstract></record></records></xml>