The Mathematics and Computer Science Department at the Faculty of Science, Beirut Arab University, Lebanon is excited to announce the second seminar event within the Math and CS Seminar Series which will be presented by Dr. Aissa Gusemia, Associate Professor of Mathematics at Elie Cartan Institute at Lorraine, France.
Topic:
Cauchy Systems Of Type Rao-Nakra Sandwich Beam With Frictional Dampings Or Infinite Memories
Date and Time:
Friday, Dec. 1, 2023, at 1:00 PM
Zoom:
https://zoom.us/j/96417417775?pwd=bEd3WmFsNlZyWGh2WXpBTVd6MUhDZz09
Abstract:
The objective of this work is to study the stability of two systems of type Rao-Nakra sandwich beam in the whole line R with a frictional damping or an infinite memory acting on the Euler-Bernoulli equation. When the speeds of propagation of the two wave equations are equal, we show that the solutions do not converge to zero when time goes to infinity. In the reverse situation, we prove some L2(R)-norm and L1(R)-norm decay estimates of solutions and their higher-order derivatives with respect to the space variable. Thanks to interpolation inequalities and Carlson inequality, these L2(R)-norm and L1(R)-norm decay estimates lead to similar ones in the Lq(R)-norm, for any q in [1;+inf]. In both L2(R)-norm and L1(R)-norm decay estimates, we specify the decay rates in terms of the regularity of the initial data and the nature of the control. Applications to some Cauchy Timoshenko type systems will be also given. The proof is based on the energy method combined with the Fourier analysis (by using the transformation in the Fourier space and well-chosen multipliers).
Biography:
Dr. Aissa Gusemia is an Associate Professor of Mathematics at Elie Cartan Institute of Lorraine, France. He obtained a Bachelor's degree in June 1991 with a specialization in Technical Mathematics from Technicome de M'sila in Algeria. Subsequently, he pursued a four-year mathematics program at Ferhat Abbas University in Setif, Algeria, earning a Diploma of Higher Studies (DES) in Mathematics with a focus on Functional Analysis. As the top graduate in his class, he secured a French government scholarship for four years to pursue a Master's (Diplôme d'Etudes Approfondies - DEA) and a Ph.D. in Mathematics in France. He spent six years at the University of Strasbourg, completing his studies in October 2001. The Ph.D. thesis, defended on November 15, 2000, was titled "Contributions to Exact Controllability and Stabilization of Evolutionary Systems." Afterward, he engaged in teaching roles at the University of Strasbourg, first as a part-time lecturer and later as an Attaché Temporaire d'Enseignement et de Recherche (ATER) for two years. Following his success in the competition for a Lecturer position, he joined the University of Lorraine-Metz in September 2001. Over the next five years, alongside teaching and collective responsibilities, he prepared and defended his Habilitation à Diriger des Recherches (HDR) thesis on "Integral Inequalities and Applications to the Stabilization of Non-Dissipative Distributed Systems" on October 31, 2006.
His research activities, marked by numerous publications, conference participations, and collaborations, have focused on various problems in Partial Differential Equations (PDE) and control theory. Additionally, he contributed significantly to international collaborations, including teaching in Algeria, Saudi Arabia, Lebanon, and Oman. He supervised several Algerian students, both for master's theses and doctoral dissertations, fostering academic development and research collaboration between Algeria and France. Dr. Guesmia established collaborations with universities worldwide, including Lebanon, Oman, Saudi Arabia, Brazil, Chile, and the United States. Notably, he spent two years as an Associate Professor at King Fahd University of Petroleum and Minerals (KFUPM) and received an Adjunct Professor position in September 2019, indicating a continuing and intensified collaboration. Besides research and teaching, he actively participated in organizing scientific events, took on pedagogical and scientific responsibilities within the mathematics department at the University of Lorraine-Metz, and engaged in various departmental activities. His commitment extended to regular attendance at seminars, workshops, and departmental meetings, contributing to the academic community's growth.
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