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This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art. Applied mathematicians and advanced graduate students wishing to enter the field of VIs would benefit from this work as it sets out in detail basic features and results in the mathematical theory of contact mechanics. Researchers interested in applications of numerical analysis pertaining to VIs would also find the work useful. Assuming a reasonable knowledge of functional analysis, this volume is a must for graduate students, practitioners, and engineers engaged in contact mechanics.

Variational inequalities (Mathematics). --- Variational inequalities (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Differential inequalities. --- Inequalities, Variational (Mathematics) --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Operator theory. --- Partial differential equations. --- Calculus of variations. --- Continuum mechanics. --- Calculus of Variations and Optimal Control; Optimization. --- Analysis. --- Continuum Mechanics and Mechanics of Materials. --- Global Analysis and Analysis on Manifolds. --- Operator Theory. --- Partial Differential Equations. --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Partial differential equations --- Functional analysis --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Inequalities (Mathematics) --- Calculus of variations --- Differential inequalities --- Mathematical optimization. --- Mechanics. --- Mechanics, Applied. --- Global analysis. --- Differential equations, partial. --- Solid Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal

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Differential geometry. Global analysis --- Operator theory --- Partial differential equations --- Numerical methods of optimisation --- Fluid mechanics --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie --- kansrekening --- mechanica --- optimalisatie

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Highlighting recent advances in variational and hemivariational inequalities with an emphasis on theory, numerical analysis and applications, this volume serves as an indispensable resource to graduate students and researchers interested in the latest results from recognized scholars in this relatively young and rapidly-growing field. Particularly, readers will find that the volume’s results and analysis present valuable insights into the fields of pure and applied mathematics, as well as civil, aeronautical, and mechanical engineering. Researchers and students will find new results on well posedness to stationary and evolutionary inequalities and their rigorous proofs. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities. Finally, the applications presented illustrate the use of these results in the study of miscellaneous mathematical models which describe the contact between deformable bodies and a foundation. This includes the modelling, the variational and the numerical analysis of the corresponding contact processes. Furthermore, it can be used as supplementary reading material for advanced specialized courses in mathematical modeling for students with a strong background knowledge on nonlinear analysis, numerical analysis, partial differential equations, and mechanics of continua.

Mathematics. --- Combinatorics. --- Mathematical Modeling and Industrial Mathematics. --- Operator Theory. --- Operator theory. --- Mathématiques --- Théorie des opérateurs --- Hemivariational inequalities. --- Relaxation methods (Mathematics). --- Variational inequalities (Mathematics). --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Variational inequalities (Mathematics) --- Inequalities, Hemivariational --- Inequalities, Variational (Mathematics) --- Mathematical models. --- Combinatorics --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Functional analysis --- Math --- Science --- Calculus of variations --- Differential inequalities