An Introduction to Theory and Applications of Stationary Variational-Hemivariational Inequalities

2024
ISBN: 978-3-031-74215-6
Verlag: Springer Nature Switzerland

Buch, Englisch, Band 220, 254 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 571 g

Reihe: Applied Mathematical Sciences

This book offers a comprehensive and accessible introduction to the mathematical theory of stationary Variational-Hemivariational Inequalities (VHIs), a rapidly growing area of research with significant applications in science and engineering. Unlike traditional approaches that rely heavily on abstract inclusion results for pseudomonotone operators, this work presents a more user-friendly method grounded in basic Functional Analysis. VHIs include variational inequalities and hemivariational inequalities as special cases. The book systematically categorizes and names different VHIs, making it easier for readers to understand the specific problems being addressed.

Designed for graduate students and researchers in mathematics, physical sciences, and engineering, this monograph not only provides a concise review of essential materials in Sobolev spaces, convex analysis, and nonsmooth analysis but also delves into applications in contact and fluid mechanics. Through detailed explanations and practical examples, the book bridges the gap between theory and practice, making the complex subject of VHIs more approachable.

By focusing on the well-posedness of various forms of VHIs and extending the analysis to include mixed VHIs for the Stokes and Navier-Stokes equations, this book serves as an essential resource for anyone interested in the modeling, analysis, numerical solutions, and real-world applications of VHIs.

Zielgruppe

Research

Autoren/Hrsg.

Han, Weimin

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre

Inhaltsverzeichnis

Preface.- Introduction.- Preliminaries.- Scalar Variational-hemivariational Inequalities.- Models in Contact Mechanics.- Variational-hemivariational Inequalities: Existence and Uniqueness.- Variational-hemivariational Inequalities: Stability.- Mixed Variational-Hemivariational Inequalities.- Applications in Fluid Mechanics.- References.- Index.

Über Autor(innen)

Weimin Han is a Professor of Mathematics and Collegiate Fellow at the University of Iowa, and a Fellow of the American Mathematical Society. His current research interests are in interdisciplinary applied mathematics, numerical analysis, computational mechanics, computational engineering, especially in analysis, numerical solution and applications of variational-hemivariational inequalities. He has co-authored twelve books and over 220 research papers in peer-reviewed journals.