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Variational Inequalities And Flow In Porous Media
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Book Synopsis Variational Inequalities and Flow in Porous Media by : M. Chipot
Download or read book Variational Inequalities and Flow in Porous Media written by M. Chipot and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Variational Inequalities and Flow in Porous Media by : Michel Chipot
Download or read book Variational Inequalities and Flow in Porous Media written by Michel Chipot and published by . This book was released on 1984 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Variational Inequalities and Their Applications by : David Kinderlehrer
Download or read book An Introduction to Variational Inequalities and Their Applications written by David Kinderlehrer and published by SIAM. This book was released on 2000-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.
Book Synopsis Variational-Hemivariational Inequalities with Applications by : Mircea Sofonea
Download or read book Variational-Hemivariational Inequalities with Applications written by Mircea Sofonea and published by CRC Press. This book was released on 2024-12-23 with total page 961 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational-Hemivariational Inequalities with Applications, Second Edition represents the outcome of the cross-fertilization of nonlinear functional analysis and mathematical modelling, demonstrating its application to solid and contact mechanics. Based on authors’ original results, the book illustrates the use of various functional methods (including monotonicity, pseudomonotonicity, compactness, penalty and fixed-point methods) in the study of 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, this book is also a valuable tool for graduate students and researchers in nonlinear analysis, mathematical modelling, mechanics of solids, and contact mechanics. New to the second edition Convergence and well-posedness results for elliptic and history-dependent variational-hemivariational inequalities Existence results on various optimal control problems with applications in solid and contact mechanics Existence, uniqueness and stability results for evolutionary and differential variational-hemivariational inequalities with unilateral constraints Modelling and analysis of static and quasistatic contact problems for elastic and viscoelastic materials with looking effect Modelling and analysis of viscoelastic and viscoplastic dynamic contact problems with unilateral constraints.
Book Synopsis Mathematical Modeling for Flow and Transport Through Porous Media by : Gedeon Dagan
Download or read book Mathematical Modeling for Flow and Transport Through Porous Media written by Gedeon Dagan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this paper is to present some new and general results, ap plicable to the the equations of two phase flow, as formulated in geothermal reservoir engineering. Two phase regions are important in many geothermal reservoirs, especially at depths of order several hundred metres, where ris ing, essentially isothermal single phase liquid first begins to boil. The fluid then continues to rise, with its temperature and pressure closely following the saturation (boiling) curve appropriate to the fluid composition. Perhaps the two most interesting theoretical aspects of the (idealised) two phase flow equations in geothermal reservoir engineering are that firstly, only one component (water) is involved; and secondly, that the densities of the two phases are so different. This has led to the approximation of ignoring capillary pressure. The main aim of this paper is to analyse some of the consequences of this assumption, especially in relation to saturation changes within a uniform porous medium. A general analytic treatment of three dimensional flow is considered. Pre viously, three dimensional modelling in geothermal reservoirs have relied on numerical simulators. In contrast, most of the past analytic work has been restricted to one dimensional examples.
Book Synopsis Mathematical Theory of Hemivariational Inequalities and Applications by : Zdzistaw Naniewicz
Download or read book Mathematical Theory of Hemivariational Inequalities and Applications written by Zdzistaw Naniewicz and published by CRC Press. This book was released on 1994-11-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives a complete and rigorous presentation of the mathematical study of the expressions - hemivariational inequalities - arising in problems that involve nonconvex, nonsmooth energy functions. A theory of the existence of solutions for inequality problems involving monconvexity and nonsmoothness is established.
Book Synopsis A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling by : Jörg Steinbach
Download or read book A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling written by Jörg Steinbach and published by Birkhäuser. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies an evolutionary variational inequality approach to a degenerate moving free boundary problem. It takes an intermediate position between elliptic and parabolic inequalities and comprises an elliptic differential operator, a memory term and time-dependent convex constraint sets. Finally, a description of injection and compression moulding is presented in terms of different mathematical models, a generalized Hele-Shaw flow, a distance concept and Navier-Stokes flow.
Book Synopsis Variational Inequalities and Frictional Contact Problems by : Anca Capatina
Download or read book Variational Inequalities and Frictional Contact Problems written by Anca Capatina and published by Springer. This book was released on 2014-09-16 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the investigation of more general classes of variational inequalities. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems. Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in an almost exhaustive way. The readers will find a systematic and unified exposition on classical, variational and dual formulations, existence, uniqueness and regularity results, finite element approximations and related optimal control problems. This part of the book is an update of the Signorini problem with nonlocal Coulomb friction, a problem little studied and with few results in the literature. Also, in the quasi-static case, a control problem governed by a bilateral contact problem is studied. Despite the theoretical nature of the presented results, the book provides a background for the numerical analysis of contact problems. The materials presented are accessible to both graduate/under graduate students and to researchers in applied mathematics, mechanics, and engineering. The obtained results have numerous applications in mechanics, engineering and geophysics. The book contains a good amount of original results which, in this unified form, cannot be found anywhere else.
Book Synopsis Vector Variational Inequalities and Vector Optimization by : Qamrul Hasan Ansari
Download or read book Vector Variational Inequalities and Vector Optimization written by Qamrul Hasan Ansari and published by Springer. This book was released on 2017-10-31 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
Book Synopsis Modelling Water Flow in Unsaturated Porous Media by : Adam Szymkiewicz
Download or read book Modelling Water Flow in Unsaturated Porous Media written by Adam Szymkiewicz and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on two issues related to mathematical and numerical modelling of flow in unsaturated porous media. In the first part numerical solution of the governing equations is discussed, with particular emphasis on the spatial discretization of highly nonlinear permeability coefficient. The second part deals with large scale flow in heterogeneous porous media of binary structure. Upscaled models are developed and it is shown that the presence of material heterogeneities may give rise to additional non-equilibrium terms in the governing equations or to hysteresis in the averaged constitutive relationships.
Book Synopsis Functional Analysis and Applications by : Abul Hasan Siddiqi
Download or read book Functional Analysis and Applications written by Abul Hasan Siddiqi and published by Springer. This book was released on 2018-05-04 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.
Book Synopsis Numerical Analysis of Variational Inequalities by : R. Trémolières
Download or read book Numerical Analysis of Variational Inequalities written by R. Trémolières and published by Elsevier. This book was released on 2011-08-18 with total page 807 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Analysis of Variational Inequalities
Book Synopsis Grants and Awards for the Fiscal Year Ended ... by : National Science Foundation (U.S.)
Download or read book Grants and Awards for the Fiscal Year Ended ... written by National Science Foundation (U.S.) and published by . This book was released on 1977 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Functional Analysis by : Abul Hasan Siddiqi
Download or read book Applied Functional Analysis written by Abul Hasan Siddiqi and published by CRC Press. This book was released on 2003-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1975 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Methods for Set-valued Nonlinear Analysis by : Enayet Ullah Tarafdar
Download or read book Topological Methods for Set-valued Nonlinear Analysis written by Enayet Ullah Tarafdar and published by World Scientific. This book was released on 2008 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems.Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings.
Book Synopsis Nonlinear Partial Differential Equations with Applications by : Tomás Roubicek
Download or read book Nonlinear Partial Differential Equations with Applications written by Tomás Roubicek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
