Minimax Theorems And Qualitative Properties Of The Solutions Of Hemivariational Inequalities
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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 : 1999
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 1999 with Mathematics categories.
The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e. involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is self-contained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers.
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.
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.
Advances In Variational And Hemivariational Inequalities
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Author : Weimin Han
language : en
Publisher: Springer
Release Date : 2015-03-02
Advances In Variational And Hemivariational Inequalities written by Weimin Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-02 with Mathematics categories.
This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.
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.
Variational And Non Variational Methods In Nonlinear Analysis And Boundary Value Problems
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Author : Dumitru Motreanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Variational And Non Variational Methods In Nonlinear Analysis And Boundary Value Problems 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 2013-06-29 with Mathematics categories.
This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.
Error Control Adaptive Discretizations And Applications Part 3
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Author :
language : en
Publisher: Academic Press
Release Date : 2025-06-16
Error Control Adaptive Discretizations And Applications Part 3 written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-16 with Science categories.
Error Control, Adaptive Discretizations, and Applications, Volume 60, Part Three highlights new advances, with this volume presenting interesting chapters written by an international board of authors. Chapters in this release cover Higher order discontinuous Galerkin finite element methods for the contact problems, Anisotropic Recovery-Based Error Estimators and Mesh Adaptation Tailored for Real-Life Engineering Innovation, Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations, A posteriori error analysis for Finite Element approximation of some groundwater models Part I: Linear models, A posteriori error estimates for low frequency electromagnetic computations, and more.Other sections delve into A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs and Recovery techniques for finite element methods. - Covers multi-scale modeling - Includes updates on data-driven modeling - Presents the latest information on large deformations of multi-scale materials
The Mountain Pass Theorem
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Author : Youssef Jabri
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15
The Mountain Pass Theorem written by Youssef Jabri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Mathematics categories.
This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.
System Modeling And Optimization
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Author : John Cagnol
language : en
Publisher: Springer
Release Date : 2006-01-15
System Modeling And Optimization written by John Cagnol and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-15 with Technology & Engineering categories.
System Modeling and Optimization is an indispensable reference for anyone interested in the recent advances in these two disciplines. The book collects, for the first time, selected articles from the 21st and most recent IFIP TC 7 conference in Sophia Antipolis, France. Applied mathematicians and computer scientists can attest to the ever-growing influence of these two subjects. The practical applications of system modeling and optimization can be seen in a number of fields: environmental science, transport and telecommunications, image analysis, free boundary problems, bioscience, and non-cylindrical evolution control, to name just a few. New developments in each of these fields have contributed to a more complex understanding of both system modeling and optimization. Editors John Cagnol and Jean-Paul Zolésio, chairs of the conference, have assembled System Modeling and Optimization to present the most up-to-date developments to professionals and academics alike.
Nonlinear Analysis And Global Optimization
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Author : Themistocles M. Rassias
language : en
Publisher: Springer Nature
Release Date : 2021-02-26
Nonlinear Analysis And Global Optimization written by Themistocles M. Rassias and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-26 with Mathematics categories.
This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.