Almost Periodicity and Almost Automorphy: for Evolution Equations and Partial Functional Differential Equations

When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.

Abdallah Afoukal recently received a PhD from the Faculty of Sciences and Technologies at the University Sultan Moulay Slimane, Beni Mellal, Morocco. His research focuses on the analysis of abstract evolution equations and delay systems, with an emphasis on the development of results from the dynamical systems viewpoint, numerical analysis, and applications.

Brahim Es-sebbar is an Assistant Professor of Mathematics at Cadi Ayyad University, Marrakech, Morocco. He specializes in dynamical systems, differential equations, and almost periodic oscillations, with a focus on functional analysis and operator theory. He earned his PhD in 2016, and his research has been published in several international journals. His work explores the asymptotic behavior of solutions in various dynamical systems. He is also involved in teaching undergraduate and graduate-level mathematics courses.

Khalil Ezzinbi received his PhD in mathematics from Cadi Ayyad University in 1997 .He became a full professor in 2001. His research interests are evolution equations, operator theory, partial functional differential equations, dynamical systems, and integrodifferential equations. He serves as an editor-in-chief and/or an associate editor for several mathematical journals. He has been visiting professor at numerous universities at African, Asian, European and North American Universities. He has been a member of the African Academy of Sciences since 2009.Khalil has supervised several Ph.D. students from countries such as Morocco, Senegal, Tchad, Nigeria, Cameroun, Burkina Faso, Tunisia and Algeria, and has been on several doctoral dissertation committees in Africa.

Gaston M. N'Guérékata is a University Distinguished Professor of Mathematics at Morgan State University in Baltimore, MD. He received his college education at the University of Montreal in Canada then went to the University of California at Berkeley as a Fulbright scholar. Dr. N’Guerekata has served as the mathematics department chair for six years and Associated Dean in the School of Computer, Mathematical and Natural Sciences for fourteen years. He is an American Mathematical Society (AMS) fellow, The World Academy of Sciences (TWAS) fellow, African Academy of Sciences (AAS) fellow, and Pan African Scientific Research Council (PASRC) fellow. Dr. N’Guerekata authored 320 publications including 14 books at the graduate/research level with Springer, World Scientific, and Nova Science Publishers. His books on almost automorphy are cornerstones in the area. He received several honors including the French Legion of Honor, Memento of Honor at the 106th Indian Science Congress, the NAFEO Noble Award, the Dr. Iva Jones Medallion, the Dr. Santire Jean McIntyre International award and the A.B. Roy Lifetime Achievement Award for the development of mathematics worldwide from Jadavpur university, Kolkata, India. Recently, the African Mathematical Union created a competitive award after his name, the so-called "N’Guerekata Award for Excellence in Mathematics". Dr. N’Guerekata is a member of the editorial board of over 21 international peer-reviewed journals. He graduated ten Ph.D. students and several master’s students and served on AMS committees as chair or member, including the Committee on Publications (Cpub), the Gibbs lecture series committee, the Canvassing committee, and the Simon PUI committee.