Energy Research Abstracts
Author:
Publisher:
Published: 1991
Total Pages: 1030
ISBN-13:
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Fixed Point Theory, Variational Analysis, and Optimization
Author: Saleh Abdullah R. Al-Mezel
Publisher: CRC Press
Published: 2014-06-03
Total Pages: 368
ISBN-13: 1482222086
DOWNLOAD EBOOKFixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis-fixed point theory, variational inequalities, and vector optimization-but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions invol
Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
Author: R. E. Showalter
Publisher: American Mathematical Soc.
Published: 2013-02-22
Total Pages: 296
ISBN-13: 0821893971
DOWNLOAD EBOOKThe objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.
Hemivariational Inequalities
Author: Panagiotis D. Panagiotopoulos
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 453
ISBN-13: 3642516777
DOWNLOAD EBOOKThe aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.
Variational and Quasivariational Inequalities
Author: C. Baiocchi
Publisher: John Wiley & Sons
Published: 1984
Total Pages: 472
ISBN-13:
DOWNLOAD EBOOKNonlinear Operators and the Calculus of Variations
Author: J.P. Gossez
Publisher: Springer
Published: 2006-11-14
Total Pages: 247
ISBN-13: 3540380752
DOWNLOAD EBOOKImpulse Control and Quasi-variational Inequalities
Author: Alain Bensoussan
Publisher: Bordas Editions
Published: 1984
Total Pages: 712
ISBN-13:
DOWNLOAD EBOOK"The general aim of this book is to establish and study the relations that exist, via dynamic programming, between, on the one hand, stochastic control, and on the other hand variational and quasi-variational inequalities, with the intention of obtaining constructive methods of solution by numerical methods. It begins with numerous examples which occur in applications and goes on to study, from an analytical viewpoint, both elliptic and parabolic quasi-variational inequalities. Finally the authors reconstruct an optimal control starting from the solution of the quasi-variational inequality."--Amazon.
Uncertainty Quantification in Variational Inequalities
Author: Joachim Gwinner
Publisher: CRC Press
Published: 2021-12-21
Total Pages: 334
ISBN-13: 1351857665
DOWNLOAD EBOOKUncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature
Variational Analysis
Author: R. Tyrrell Rockafellar
Publisher: Springer Science & Business Media
Published: 2009-06-26
Total Pages: 747
ISBN-13: 3642024319
DOWNLOAD EBOOKFrom its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Handbook of Generalized Convexity and Generalized Monotonicity
Author: Nicolas Hadjisavvas
Publisher: Springer Science & Business Media
Published: 2006-01-16
Total Pages: 684
ISBN-13: 0387233938
DOWNLOAD EBOOKStudies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.
