Variational-Hemivariational Inequalities with Applications

by Mircea Sofonea, Stanislaw Migorski

Overview

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.

Product Details

ISBN-13:	9781040263198
Publisher:	CRC Press
Publication date:	12/10/2024
Series:	Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	350
File size:	878 KB

About the Author

Mircea Sofonea earned his PhD from the University of Bucarest, Romania, and his habilitation at the Université Blaise Pascal of Clermont-Ferrand (France).He is currently a Distinguished Profesor of Applied Mathematics at the University of Perpignan Via Domitia, France and a honorary member of the Institute of Mathematics, Romanian Academy of Sciences. His areas of interest and expertise include multivalued operators, variational and hemivariational inequalities, solid mechanics, contact mechanics and numerical methods for partial differential equations. Most of his reseach is dedicated to the Mathematical Theory of Contact Mechanics, of which he is one of the main contributors. His ideas and results were published in nine books, four monographs, and more than three hundred research articles.

Stanislaw Migórski earned his PhD degree and the habilitation from the Jagiellonian University in Krakow, Poland. He is currently a Full Honorary Professor and Chair of Optimization and Control Theory at Jagiellonian University in Krakow. His areas of interest and expertise include mathematical analysis, differential equations, mathematical modelling, methods and technics of nonlinear analysis, homogenization, control theory, computational methods and pplications of partial differential equations to mechanics. His research results are internationally recognized and were published in six books, four monographs, and more than two hundred research articles.

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.

Editorial Reviews

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

From the Publisher