Inequality Problems In Mechanics And Applications

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Inequality Problems In Mechanics And Applications

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Author : P.D. Panagiotopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-01-01

Inequality Problems In Mechanics And Applications written by P.D. Panagiotopoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.

In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J. L. Lions, G. Maier, J. J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H. O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript.

Inequality Problems In Mechanics And Applications

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Author : Panagiotis D. Panagiotopoulos
language : en
Publisher:
Release Date : 1985

Inequality Problems In Mechanics And Applications written by Panagiotis D. Panagiotopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.

Inequality Problems In Mechanics And Applications

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Author : P.D. Panagiotopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Inequality Problems In Mechanics And Applications written by P.D. Panagiotopoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J. L. Lions, G. Maier, J. J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H. O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript.

Minimax Theorems And Qualitative Properties Of The Solutions Of Hemivariational Inequalities

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Author : Dumitru Motreanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Minimax Theorems And Qualitative Properties Of The Solutions Of Hemivariational Inequalities written by Dumitru Motreanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

Boundary value problems which have variational expressions in form of inequal ities can be divided into two main classes. The class of boundary value prob lems (BVPs) leading to variational inequalities and the class of BVPs leading to hemivariational inequalities. The first class is related to convex energy functions and has being studied over the last forty years and the second class is related to nonconvex energy functions and has a shorter research "life" beginning with the works of the second author of the present book in the year 1981. Nevertheless a variety of important results have been produced within the framework of the theory of hemivariational inequalities and their numerical treatment, both in Mathematics and in Applied Sciences, especially in Engineering. It is worth noting that inequality problems, i. e. BVPs leading to variational or to hemivariational inequalities, have within a very short time had a remarkable and precipitate development in both Pure and Applied Mathematics, as well as in Mechanics and the Engineering Sciences, largely because of the possibility of applying and further developing new and efficient mathematical methods in this field, taken generally from convex and/or nonconvex Nonsmooth Analy sis. The evolution of these areas of Mathematics has facilitated the solution of many open questions in Applied Sciences generally, and also allowed the formu lation and the definitive mathematical and numerical study of new classes of interesting problems.

Variational And Hemivariational Inequalities Theory Methods And Applications

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Author : D. Goeleven
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27

Variational And Hemivariational Inequalities Theory Methods And Applications written by D. Goeleven and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.

An Introduction To Theory And Applications Of Stationary Variational Hemivariational Inequalities

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Author : Weimin Han
language : en
Publisher: Springer Nature
Release Date : 2024-11-01

An Introduction To Theory And Applications Of Stationary Variational Hemivariational Inequalities written by Weimin Han and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.

This book offers a comprehensive and accessible introduction to the mathematical theory of stationary Variational-Hemivariational Inequalities (VHIs), a rapidly growing area of research with significant applications in science and engineering. Unlike traditional approaches that rely heavily on abstract inclusion results for pseudomonotone operators, this work presents a more user-friendly method grounded in basic Functional Analysis. VHIs include variational inequalities and hemivariational inequalities as special cases. The book systematically categorizes and names different VHIs, making it easier for readers to understand the specific problems being addressed. Designed for graduate students and researchers in mathematics, physical sciences, and engineering, this monograph not only provides a concise review of essential materials in Sobolev spaces, convex analysis, and nonsmooth analysis but also delves into applications in contact and fluid mechanics. Through detailed explanations and practical examples, the book bridges the gap between theory and practice, making the complex subject of VHIs more approachable. By focusing on the well-posedness of various forms of VHIs and extending the analysis to include mixed VHIs for the Stokes and Navier-Stokes equations, this book serves as an essential resource for anyone interested in the modeling, analysis, numerical solutions, and real-world applications of VHIs.

Nonlinear Inclusions And Hemivariational Inequalities

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Author : Stanisław Migórski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-18

Nonlinear Inclusions And Hemivariational Inequalities written by Stanisław Migórski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-18 with Mathematics categories.

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Encyclopedia Of Optimization

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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04

Encyclopedia Of Optimization written by Christodoulos A. Floudas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-04 with Mathematics categories.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Finite Dimensional Variational Inequalities And Complementarity Problems

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Author : Francisco Facchinei
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14

Finite Dimensional Variational Inequalities And Complementarity Problems written by Francisco Facchinei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.

The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).

Recent Developments In Boundary Element Methods

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Author : Evangelous J. Sapountzakis
language : en
Publisher: WIT Press
Release Date : 2010

Recent Developments In Boundary Element Methods written by Evangelous J. Sapountzakis and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Technology & Engineering categories.

This Festschrift is a collection of articles contributed by colleagues, collaborators and past students to honor Professor John T. Katsikadelis on the occasion of his 70 years. Professor Katsikadelis, now an emeritus professor at the National Technical University of Athens in Greece, is one of the BEM pioneers who started his research in this field with his PhD thesis at the Polytechnic Institute of New York in the 1970s and continued it to date.The book comprises 26 contributions by more than 50 leading researchers in Boundary Element Methods (BEM) and other Mesh Reduction Methods (MRM). All contributors are well-known scientists from Asia, Australia, Europe, and North and South America. The volume is essentially a collection of both original and review articles covering a variety of research topics in the areas of solid mechanics, fluid mechanics, potential theory, composite materials, fracture mechanics, damage mechanics, plasticity, heat transfer, dynamics and vibrations and soil-structure interaction. Invaluable to scientists, engineers and other professionals interested in the latest developments of the boundary integral equation methods, it addresses the needs of the BEM computational mechanics research community.The book is written for: researchers in academia and industry and graduate students focusing on solid and fluid mechanics as used in civil, mechanical and aerospace engineering.