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Differential inclusions --- Control theory --- Mathematical optimization --- Control theory. --- Differential inclusions. --- Mathematical optimization.

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Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important onesIncludes practical examples

Approximation theory. --- Differential inclusions. --- Mathematical optimization. --- Differential inclusions --- Mathematical optimization --- Approximation theory --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Calculus --- Operations Research --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems

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Nonlinear Inclusions and Hemivariational Inequalities presents a broad insight into the theory of inclusions, hemivariational inequalities, and their applications to Contact Mechanics. The content of this volume gathers recent results which are published here for the first time and gives a largely self-contained and rigorous introduction to mathematical analysis of contact problems. The book will be of particular interest to students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and may also prove suitable as a supplementary text for an advanced one or two semester specialized course in mathematical modeling.   This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of Contact Mechanics. It covers both abstract existence and uniqueness results as well as the study of specific contact problems, including their modeling and variational analysis. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation.   The text is divided into three parts. Part I, entitled Background of Functional Analysis, gives an overview of nonlinear and functional analysis, function spaces, and calculus of nonsmooth operators. The material presented may be useful to students and researchers from a broad range of mathematics and mathematical disciplines. Part II concerns Nonlinear Inclusions and Hemivariational Inequalities and is the core of the text in terms of theory. Part III, entitled Modeling and Analysis of Contact Problems shows applications of theory in static and dynamic contact problems with deformable bodies, where the material behavior is modeled with both elastic and viscoelastic constitutive laws. Particular attention is paid to the study of contact problems with piezoelectric materials. Bibliographical notes presented at the end of each part are valuable for further study.

Mathematical models. --- Hemivariational inequalities. --- Differential inclusions. --- Inclusions, Differential --- Inequalities, Hemivariational --- Models, Mathematical --- Hemivariational inequalities --- Mathematics. --- Functional analysis. --- Partial differential equations. --- Mechanics. --- Partial Differential Equations. --- Functional Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Simulation methods --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Differentiable dynamical systems --- Differential equations --- Set-valued maps --- Differential inequalities --- Differential equations, partial. --- Classical Mechanics.

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This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature. In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems;evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail. Based on extensive research work conducted by the authors and other experts over the past four years, the information presented is cutting-edge and comprehensive. As such, the book fills an important gap in the body of literature on the structure of evolution inclusions and its applications.

Mathematics. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Probabilities. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Probability Theory and Stochastic Processes. --- Differential inclusions. --- Inclusions, Differential --- Differentiable dynamical systems --- Differential equations --- Set-valued maps --- Differential Equations. --- Differentiable dynamical systems. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- 517.91 Differential equations --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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Stochastic Differential Inclusions and Applications further develops the theory of stochastic functional inclusions and their applications. This self-contained volume is designed to systematically introduce the reader from the very beginning to new methods of the stochastic optimal control theory. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The text presents recent and pressing issues in stochastic processes, control, differential games, and optimization that can be applied to finance, manufacturing, queueing networks, and climate control. The work is divided into seven chapters, with the first two, containing selected introductory material dealing with point- and set-valued stochastic processes. The final two chapters are devoted to applications and optimal control problems. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, this book is intended for students and researchers in mathematics and applications, particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Mathematics. --- Stochastic partial differential equations. --- Stochastic processes. --- Differential equations --- Differential equations, Partial --- Numerical analysis --- Mathematical optimization --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Calculus --- Differential equations. --- Differential equations, Partial. --- Partial differential equations --- 517.91 Differential equations --- Math --- Random processes --- Banach spaces, Stochastic differential equations in --- Hilbert spaces, Stochastic differential equations in --- SPDE (Differential equations) --- Stochastic differential equations in Banach spaces --- Stochastic differential equations in Hilbert spaces --- Partial differential equations. --- Numerical analysis. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Ordinary Differential Equations. --- Numerical Analysis. --- Partial Differential Equations. --- Science --- Probabilities --- Mathematical optimization. --- Differential Equations. --- Differential equations, partial. --- Mathematical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Isoperimetrical problems --- Variations, Calculus of --- Stochastic control theory. --- Differential inclusions.