Advances in Nonlinear Evolution Equations

This book presents a collection of significant and original contributions that delve into the realm of nonlinear evolution equations and their applications, encompassing both theory and practical usage. Serving as a dynamic platform for interdisciplinary collaboration, it facilitates the exchange of innovative ideas among scientists from diverse fields who share a keen interest in the intricate world of evolution equations. The book bridges the gap between theory and practicality, offering valuable insights for researchers and enthusiasts alike, transcending disciplinary boundaries. Evolution equations, a subset of partial differential equations, serve as mathematical tools to depict the temporal transformation of physical systems from their initial states. These equations find widespread utility in modeling various real-world phenomena across diverse disciplines. Notable examples of nonlinear evolution equations include the heat equation, which characterizes the evolution of heat distribution over time; the nonlinear Schrödinger equation, instrumental in understanding data transmission in fiber optic communication systems; the Korteweg-de Vries equation, illuminating the dynamics of surface water waves; and the portrayal of ion-acoustic waves in cold plasma.

Mohamed Jleli is Full Professor of Mathematics at King Saud University, Riyadh, Saudi Arabia. He received his Ph.D. in Mathematics with the thesis entitled “Constant Mean Curvature Hypersurfaces” from the Faculty of Sciences of Paris VI, France, in 2004. His research interests include surfaces and hypersurfaces in space forms, mean curvature, nonlinear partial differential equations, nonlinear fractional calculus and nonlinear analysis, in which he has published his research articles in international journals of repute. He is on the editorial board of several international journals of mathematics.

Bessem Samet is Full Professor of Applied Mathematics at King Saud University, Riyadh, Saudi Arabia. He received his Ph.D. in Mathematics with the thesis entitled “Topological Derivative Method for Maxwell Equations and its Applications” from Paul Sabatier University, France, in 2004. His areas of research include different branches of nonlinear analysis, including functional analysis, partial differential equations, fractional calculus, etc. He has authored/co-authored more than 100 research papers in reputed journals. He is on the list of Thomson Reuters Highly Cited Researchers for the year 2021 (also for the years 2015–2017).

Calogero Vetro is Associate Professor of Mathematical Analysis at the University of Palermo, Italy, since 2005. He is also affiliated with the Department of Mathematics and Computer Science of the university. He received his Ph.D. in Engineering of Automation and Control Systems in 2004 and the Laurea Degree in Mechanical Engineering in 2000. He has taught courses in mathematical analysis, numerical analysis, numerical calculus, geomathematics, computational mathematics, operational research and optimization. He is Member of the Doctoral Collegium at the University of Palermo and acts as Referee for several scientific journals of mathematics. He is also on the editorial boards of renowned scientific journals and Guest Editor of special issues on fixed point theory and partial differential equations. His research interests include approximation, fixed point theory, functional analysis, mathematical programming, operator theory and partial differential equations. He has authored/co-authored more than 150 papers and was on the Thomson Reuters Highly Cited Researchers List from 2015–2017.