Panagiotis D. Panagiotopoulos Knihy

This book explores the formulation and numerical analysis of static and dynamic problems in mechanics and engineering that involve complex energy functions and multivalued stress-strain laws. It introduces hemivariational inequalities and presents innovative numerical methods to tackle real-world engineering challenges, such as adhesive contact in cracks and delamination issues. Additionally, it discusses the mathematical foundations, existence results, and optimal control problems related to these inequalities, concluding with applications in fractal geometries and neural network approaches.

The book explores boundary value problems (BVPs) categorized into variational and hemivariational inequalities, emphasizing their distinct characteristics. The variational inequalities relate to convex energy functions, while hemivariational inequalities address nonconvex scenarios, a field that emerged in 1981. It highlights the rapid advancements in both theoretical and applied mathematics, particularly in engineering, due to the introduction of innovative mathematical methods. The text showcases significant progress in solving complex problems across various scientific disciplines.

This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan.