<?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%">Belkacem Aksas</style></author><author><style face="normal" font="default" size="100%">Salah-eddine Rebiai</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Uniform stabilization of the fourth order Schrödinger equation</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Mathematical Analysis and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><volume><style face="normal" font="default" size="100%">446</style></volume><pages><style face="normal" font="default" size="100%">1794-1813</style></pages><isbn><style face="normal" font="default" size="100%">0022-247X</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">2</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%">Belkacem Aksas</style></author><author><style face="normal" font="default" size="100%">Salah-eddine Rebiai</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Stabilization of the Fourth Order Schrödinger Equation</style></title><secondary-title><style face="normal" font="default" size="100%">New Trends in Analysis and Interdisciplinary Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><pages><style face="normal" font="default" size="100%"> 529-535</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 study both boundary and internal stabilization problems for the fourth order Schrödinger equation in a smooth bounded domain&amp;nbsp;Ω&amp;nbsp;of&amp;nbsp;R&lt;sup&gt;n&lt;/sup&gt;.&amp;nbsp;We first consider the boundary stabilization problem. By introducing suitable dissipative boundary conditions, we prove that the solution decays exponentially in an appropriate energy space. In the internal stabilization problem, by assuming that the damping term is effective on the neighborhood of the boundary, we prove the exponential decay of the L&lt;sup&gt;2&lt;/sup&gt;(Ω)-energy of the solution. Both results are established by using multipliers technique and compactness/uniqueness arguments.
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