<?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%">Saci,  Atef</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An inverse problem for the Schrödinger equation with Neumann boundary condition</style></title><secondary-title><style face="normal" font="default" size="100%">Advances in Pure and Applied Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.openscience.fr/IMG/pdf/iste_apam23v14n1_4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">50-69</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;
	Thisarticleconcernstheinverse problem of the recoveryof unknown potential coefficient for the Schrödinger equation, in a bounded domain of Rn with non-homogeneous Neumann boundary condition from a time-dependent Dirich let boundary measurement. We prove uniqueness and Lipschitz stability for this inverse problem under certain convexity hypothesis on the geometry of the spatial domain and under weak regularity requirements on the data. The proof is based on aCarleman estimate in [12] for Schrödinger equations and its resulting implication, a continuous observability inequality. Mathematics Subject Classification. 35R30, 35Q40, 49K20.
&lt;/p&gt;
</style></abstract><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%">Moumen, Latifa</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Exponential stability of the transmission wave equation with a distributed delay term in the boundary damping</style></title><secondary-title><style face="normal" font="default" size="100%">Rendiconti del circolo matematico di palermo series 2</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s12215-022-00834-8</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">72</style></volume><pages><style face="normal" font="default" size="100%">3459–3486</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 distributed delay term and that acts on the exterior boundary. We prove under some assumptions that the solutions decay exponentially in an appropriate energy space. To establish this result, we introduce a suitable energy function and use multipliers technique method and compactness-uniqueness argument.
&lt;/p&gt;
</style></abstract></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%">Ghecham, Wassila</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</style></author><author><style face="normal" font="default" size="100%">Ali, Fatima Zohra Sidi</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Stabilization of coupled wave equations with boundary or internal distributed delay</style></title><secondary-title><style face="normal" font="default" size="100%">Applicable AnalysisApplicable Analysis</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2021</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">14</style></number><volume><style face="normal" font="default" size="100%">100</style></volume><pages><style face="normal" font="default" size="100%">3096-3115</style></pages><isbn><style face="normal" font="default" size="100%">0003-6811</style></isbn><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%">Ghecham, Wassila</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</style></author><author><style face="normal" font="default" size="100%">SidiAli, Fatima-Zohra</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Stabilization of the wave equation with a nonlinear delay term in the boundary conditions</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Applied AnalysisJournal of Applied Analysis</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2021</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.degruyter.com/document/doi/10.1515/jaa-2021-2051/html</style></url></web-urls></urls><isbn><style face="normal" font="default" size="100%">1869-6082</style></isbn><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;
	A wave equation in a bounded and smooth domain of&amp;nbsp;Rnℝ&amp;nbsp;with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.
&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ghecham, Wassila</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</style></author><author><style face="normal" font="default" size="100%">Ali, Fatima Zohra Sidi</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Uniform boundary stabilization of the wave equation with a nonlinear delay term in the boundary conditions</style></title><secondary-title><style face="normal" font="default" size="100%">Analysis, Probability, Applications, and Computation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2019</style></date></pub-dates></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pages><style face="normal" font="default" size="100%">561-568</style></pages><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>10</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ghecham, Wassila</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</style></author><author><style face="normal" font="default" size="100%">Ali, Fatima Zohra Sidi</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Uniform boundary stabilization of the Schrödinger equation with a nonlinear delay term in the boundary conditions</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2018</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>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Aksas, Belkacem</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</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 ApplicationsNew Trends in Analysis and Interdisciplinary Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pages><style face="normal" font="default" size="100%">529-535</style></pages><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%">Aksas, Belkacem</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</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 ApplicationsNew Trends in Analysis and Interdisciplinary Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></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%">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;Rn.&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 L2(Ω)-energy of the solution. Both results are established by using multipliers technique and compactness/uniqueness arguments.</style></abstract></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%">Aksas, Belkacem</style></author><author><style face="normal" font="default" size="100%">Rebiai, Salah-Eddine</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 ApplicationsJournal of Mathematical Analysis and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">2</style></number><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></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%">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><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>10</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%">Ali, Fatima Zohra Sidi</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Exponential stability of compactly coupled wave equations with delay terms in the boundary feedbacks</style></title><secondary-title><style face="normal" font="default" size="100%">IFIP Conference on System Modeling and Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2013</style></date></pub-dates></dates><publisher><style face="normal" font="default" 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Salah-Eddine</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Boundary stabilization of the wave equation with variable coefficients</style></title><secondary-title><style face="normal" font="default" size="100%">2003 European Control Conference (ECC)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2003</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2003</style></date></pub-dates></dates><publisher><style face="normal" font="default" size="100%">IEEE</style></publisher><pages><style face="normal" font="default" size="100%">3462-3466</style></pages><isbn><style face="normal" font="default" size="100%">3-9524173-7-8</style></isbn><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 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