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E-grāmata: Variational-Hemivariational Inequalities with Applications

(University of Perpignan, France), (Jagiellonian University in Krakow, Poland)
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Variational-Hemivariational Inequalities with ApplicationsPalielināt
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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.

Recenzijas

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

Preface iii
I A Fixed Point Principle
1(104)
1 Abstract Setting and Preliminary Applications
3(28)
1.1 Statement of the principle
3(7)
1.2 Background on functional analysis
10(6)
1.3 Classical fixed point theorems
16(3)
1.4 Applications to elliptic variational inequalities
19(9)
1.5 Conclusions
28(3)
2 History-Dependent Operators
31(36)
2.1 Spaces of continuous functions
31(4)
2.2 Definitions and basic properties
35(6)
2.3 Fixed point properties
41(5)
2.4 History-dependent equations in Hilbert spaces
46(4)
2.5 Nonlinear implicit equations in Banach spaces
50(6)
2.6 History-dependent variational inequalities
56(5)
2.7 Relevant particular cases
61(6)
3 Displacement-Traction Problems in Solid Mechanics
67(38)
3.1 Modeling of displacement-traction problems
67(8)
3.2 A viscoplastic displacement-traction problem
75(7)
3.3 A viscoelastic displacement-traction problem
82(6)
3.4 History-dependent constitutive laws
88(8)
3.5 Primal variational formulation
96(3)
3.6 Dual variational formulation
99(6)
II Variational-Hemivariational Inequalities
105(100)
4 Elements of Nonsmooth Analysis
107(22)
4.1 Monotone and pseudomonotone operators
107(6)
4.2 Bochner-Lebesgue spaces
113(6)
4.3 Subgradient of convex functions
119(2)
4.4 Subgradient in the sense of Clarke
121(6)
4.5 Miscellaneous results
127(2)
5 Elliptic Variational-Hemivariational Inequalities
129(30)
5.1 A class of subdifferential inclusions
130(6)
5.2 Dual formulation
136(4)
5.3 A first existence and uniqueness result
140(2)
5.4 A general existence and uniqueness result
142(5)
5.5 A continuous dependence result
147(3)
5.6 A penalty method
150(4)
5.7 Relevant particular cases
154(5)
6 History-Dependent Variational-Hemivariational Inequalities
159(22)
6.1 An existence and uniqueness result
159(5)
6.2 A continuous dependence result
164(3)
6.3 A penalty method
167(9)
6.4 Relevant particular cases
176(5)
7 Evolutionary Variational-Hemivariational Inequalities
181(24)
7.1 A class of evolutionary inclusions
181(8)
7.2 An existence and uniqueness result
189(6)
7.3 A continuous dependence result
195(4)
7.4 Relevant particular cases
199(6)
III Applications to Contact Mechanics
205(88)
8 Static Contact Problems
207(36)
8.1 Modeling of static contact problems
207(6)
8.2 A contact problem with normal compliance
213(7)
8.3 A contact problem with subdifferential friction law
220(3)
8.4 A first contact problem with unilateral constraints
223(6)
8.5 A second contact problem with unilateral constraints
229(14)
9 Time-Dependent and Quasistatic Contact Problems
243(24)
9.1 Physical setting and mathematical models
243(2)
9.2 Two time-dependent elastic contact problems
245(8)
9.3 A quasistatic viscoplastic contact problem
253(5)
9.4 A time-dependent viscoelastic contact problem
258(2)
9.5 A quasistatic viscoelastic contact problem
260(7)
10 Dynamic Contact Problems
267(26)
10.1 A viscoelastic contact problem with normal damped response
267(11)
10.2 A viscoplastic contact problem with normal compliance
278(6)
10.3 A viscoelastic contact problem with normal compliance
284(4)
10.4 Conclusions
288(5)
Bibliography 293(14)
Index 307
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.
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