This research monograph represents an outcome of the cross-fertilization between nonlinear functional analysis and mathematical modelling, and demonstrates its application to solid and contact mechanics. Based on authors’ original results, it introduces a general fixed point principle and its application to various nonlinear problems in analysis and mechanics. The classes of history-dependent operators and almost history-dependent operators are exposed in a large generality. A systematic and unified presentation contains a carefully-selected collection of new results on variational-hemivariational inequalities with or without unilateral constraints. A wide spectrum of static, quasistatic, dynamic contact problems for elastic, viscoelastic and viscoplastic materials illustrates the applicability of these theoretical results.
Written for mathematicians, applied mathematicians, engineers and scientists, it is also a valuable tool for graduate students and researchers in nonlinear analysis, mathematical modelling, mechanics of solids, and contact mechanics.
Table of Contents
A Fixed Point Principle. Abstract Setting and Preliminary Applications. History-Dependent Operators. Displacement-Traction Problems in Solid Mechanics. Variational-Hemivariational Inequalities. Elements of Nonsmooth Analysis. Elliptic Variational-Hemivariational Inequalities. History-dependent Variational-Hemivariational Inequalities. Evolutionary Variational-Hemivariational Inequalities. Applications to Contact Mechanics. Static Contact Problems. Time-dependent and Quasistatic Contact Problems. Dynamic Contact Problems.
Professor Mircea Sofonea is Director of the Laboratoire de Mathematiques et Physique (LAMPS) and the Universite de Perpignan, France. His areas of expertise include multivalued operators, nonlinear inclusions, variational methods, variational and hemivariational inequalities, evolution equations, elasticity, viscoelasticity, viscoplasticity, contact mechanics, numerical methods. He was awarded the Prize of Blakan Union of Mathematicians in 1984 and became an Honorary Member of Institute of Mathematics of the Romanian Academy of Sciences in 2005. He has been a referee for over 50 different journals and is the author of 11 books. Professor Stanislaw Migorski is Chair and Full Professor of Mathematical Sciences at Jagiellonian University in Krakow, Poland. His areas of interest include Mathematical analysis, differential equations, mathematical modeling of various physical systems, methods and techniques of nonlinear analysis, homogenization, control theory, identifcation, computational methods, applications of partial diffferential equations to mechanics. He is the author of 3 books and contributor to a further 12.
This book presents new results concerning the xed-point theory, the study of variational-hemivariational inequalities and the study of static, quasistatic and dynamic frictional and frictionless contact problems. It provides an example of the succesful use of nonlinear functional analysis in the mathematical modeling in solid and contact mechanics. The book contains three parts.
-Ruxandra Stavre, Zentralblatt MATH