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| Author | : A. Bensoussan |
| Publisher | : Elsevier |
| Total Pages | : 577 |
| Release | : 2011-08-18 |
| Genre | : Mathematics |
| ISBN | : 0080875335 |
Applications of Variational Inequalities in Stochastic Control
| Author | : David Kinderlehrer |
| Publisher | : SIAM |
| Total Pages | : 328 |
| Release | : 2000-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898714664 |
Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.
| Author | : Anna Nagurney |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 146152301X |
Equilibrium is a concept used in operations research and economics to understand the interplay of factors and problems arising from competitive systems in the economic world. The problems in this area are large and complex and have involved a variety of mathematical methodologies. In this monograph, the authors have widened the scope of theoretical work with a new approach, `projected dynamical systems theory', to previous work in variational inequality theory. While most classical work in this area is static, the introduction to the theory of projected dynamical systems will allow many real-life dynamic situations and problems to be handled and modeled. This monograph includes: a new theoretical approach, `projected dynamical system', which allows the researcher to model real-life situations more accurately; new mathematical methods allowing researchers to combine other theoretical approaches with the projected dynamical systems approach; a framework in which research can adequately model natural, financial and human (real life) situations in competitive equilibrium problems; the computational and numerical methods for the implementation of the methods and theory discussed in the book; stability analysis, algorithms and computational procedures are offered for each set of applications.
| Author | : M. Chipot |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 127 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461211204 |
These notes are the contents of a one semester graduate course which taught at Brown University during the academic year 1981-1982. They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular case, is one of the most in teresting applications of Variational Inequalities with an obstacle. Very little background is needed to read these notes. The main re sults of functional analysis which are used here are recalled in the text. The goal of the two first chapters is to introduce the notion of Varia tional Inequality and give some applications from physical mathematics. The third chapter is concerned with a regularity theory for the obstacle problems. These problems have now invaded a large domain of applied mathematics including optimal control theory and mechanics, and a collec tion of regularity results available seems to be timely. Roughly speaking, for elliptic variational inequalities of second order we prove that the solution has as much regularity as the obstacle(s). We combine here the theory for one or two obstacles in a unified way, and one of our hopes is that the reader will enjoy the wide diversity of techniques used in this approach. The fourth chapter is concerned with the dam problem. This problem has been intensively studied during the past decade (see the books of Baiocchi-Capelo and Kinderlehrer-Stampacchia in the references). The relationship with Variational Inequalities has already been quoted above.
| Author | : C. Baiocchi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 472 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Alexander S. Kravchuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 337 |
| Release | : 2007-09-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1402063776 |
The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.
| Author | : Mircea Sofonea |
| Publisher | : CRC Press |
| Total Pages | : 412 |
| Release | : 2017-10-23 |
| Genre | : Mathematics |
| ISBN | : 1351649299 |
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.
| Author | : Vy Khoi Le |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 1997-01-24 |
| Genre | : Mathematics |
| ISBN | : 9780387948867 |
An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.
| Author | : C.j. Goh |
| Publisher | : CRC Press |
| Total Pages | : 330 |
| Release | : 2002-05-10 |
| Genre | : Mathematics |
| ISBN | : 1420018868 |
This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimizati
| Author | : Ivan Hlavacek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461210488 |
The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of mathe matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for the theory of variational inequalities, which is currently a rapidly growing branch of modern analysis. The theory of variational inequalities is a relatively young mathematical discipline. Apparently, one of the main bases for its development was the paper by G. Fichera (1964) on the solution of the Signorini problem in the theory of elasticity. Later, J. L. Lions and G. Stampacchia (1967) laid the foundations of the theory itself. Time-dependent inequalities have primarily been treated in works of J. L. Lions and H. Bnlzis. The diverse applications of the variational in equalities theory are the topics of the well-known monograph by G. Du vaut and J. L. Lions, Les iniquations en micanique et en physique (1972).
