<?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%">Farida Lombarkia</style></author><author><style face="normal" font="default" size="100%">Mohamed Amouch</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Asymmetric Fuglede Putnam's Theorem for operators reduced by their eigenspaces</style></title><secondary-title><style face="normal" font="default" size="100%">arXiv preprint arXiv:1603.07494</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language></record><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%">Salah-eddine Rebiai</style></author><author><style face="normal" font="default" size="100%">Ali, FZ Sidi</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 Information</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">OUP</style></publisher><volume><style face="normal" font="default" size="100%">33</style></volume><pages><style face="normal" font="default" size="100%">1-20</style></pages><isbn><style face="normal" font="default" size="100%">0265-0754</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">1</style></issue></record><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%">Salah-eddine Rebiai</style></author><author><style face="normal" font="default" size="100%">Fatima Zohra Sidi-Ali</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 Information</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><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%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	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.
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