Evolutionary Dynamic Equations: Stabilizability, Observability, and Controllability

The book discusses the stability, observability, and controllability of nonlinear systems of PDEs (such as Wave, Heat, Euler-Bernoulli beam, Petrovsky, Kirchhoff, equations, and more). Methods based on the theory of classical weak functions analysis and movements in Sobolev spaces are used to analyze nonlinear systems of evolutionary partial differential equations. With the unifying theme of evolutionary dynamic equations, both linear and nonlinear, in more complex environments with different approaches, the book presents a multidisciplinary blend of topics, spanning the fields of PDEs applied to various models coming from theoretical physics, biology, engineering, and natural sciences.
This comprehensive book is prepared for a diverse audience interested in applied mathematics. With its broad applicability, this book aims to foster interdisciplinary collaboration and facilitate a deeper understanding of complex phenomenon concepts, practically in electromagnetic waves, the acoustic model for seismic waves, waves in blood vessels, wind drag on space, the linear shallow water equations, sound waves in liquids and gases, non-elastic effects in the string.

Akram Ben Aissa was born on June 26, 1986, in Eljem, Tunisia. A graduate with high honors from the Faculty of Sciences in Monastir, Akram’s academic prowess earned him a Master’s degree in Mathematics in 2011. In 2016, Akram earned his Ph.D. in Mathematics from the University of Monastir. His thesis, ＂Grushin problems and Control theory of PDEs＂. Akram’s research interests span Control theory of Partial Differential Equations, Functional Analysis, and Stability and Control of PDEs. With an impressive publication record, including works on viscoelastic wave equations and second-order evolution equations, he continues to shape the mathematical landscape. In 2022, armed with a Habilitation à diriger des recherches (HdR) from the University of Sousse, he is now an associate Professor at University of Sousse, Tunisia.

Khaled Zennir was born in Algeria 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbès University, Algeria (Assist. professor). He is now associate Professor at Qassim University, KSA. His research interests lie in Nonlinear Hyperbolic Partial Differential Equations: Global Existence, Blow-Up, and Long Time Behavior.