Nonlinear And Global Analysis

Author : Themistocles M. Rassias,Panos M. Pardalos
Publisher : Springer Nature
Page : 484 pages
File Size : 42,8 Mb
Release : 2021-02-26
Category : Mathematics
ISBN : 9783030617325

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Nonlinear Analysis and Global Optimization by Themistocles M. Rassias,Panos M. Pardalos Pdf

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.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 50,8 Mb
Release : 2006
Category : Differential equations, Partial
ISBN : 9780821841433

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Nonlinear Dispersive Equations by Terence Tao Pdf

"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Author : Richard S. Palais
Publisher : Unknown
Page : 154 pages
File Size : 43,8 Mb
Release : 1968
Category : Algebras, Linear
ISBN : STANFORD:36105031262335

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Foundations of Global Non-linear Analysis by Richard S. Palais Pdf

Author : Jian-Qiao Sun,Albert C. J. Luo
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 52,8 Mb
Release : 2012-05-01
Category : Technology & Engineering
ISBN : 9781461431282

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Global Analysis of Nonlinear Dynamics by Jian-Qiao Sun,Albert C. J. Luo Pdf

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time.

Author : Felix E. Browder
Publisher : American Mathematical Soc.
Page : 644 pages
File Size : 53,5 Mb
Release : 1992
Category : Mathematics
ISBN : 0821888544

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Nonlinear and Global Analysis by Felix E. Browder Pdf

This volume contains a number of research-expository articles that appeared in the Bulletin of the AMS between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and geometry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of applications. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers in the field.

Author : Eligius M.T. Hendrix,Boglárka G.-Tóth
Publisher : Springer
Page : 208 pages
File Size : 42,8 Mb
Release : 2010-04-27
Category : Mathematics
ISBN : 9780387886701

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Introduction to Nonlinear and Global Optimization by Eligius M.T. Hendrix,Boglárka G.-Tóth Pdf

This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the presentation of numerous algorithms, examples, and illustrations, designed to improve the reader’s intuition and develop the analytical skills needed to identify optimization problems, classify the structure of a model, and determine whether a solution fulfills optimality conditions.

Author : C.S. Hsu
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 45,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475738926

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Cell-to-Cell Mapping by C.S. Hsu Pdf

For many years, I have been interested in global analysis of nonlinear systems. The original interest stemmed from the study of snap-through stability and jump phenomena in structures. For systems of this kind, where there exist multiple stable equilibrium states or periodic motions, it is important to examine the domains of attraction of these responses in the state space. It was through work in this direction that the cell-to-cell mapping methods were introduced. These methods have received considerable development in the last few years, and have also been applied to some concrete problems. The results look very encouraging and promising. However, up to now, the effort of developing these methods has been by a very small number of people. There was, therefore, a suggestion that the published material, scattered now in various journal articles, could perhaps be pulled together into book form, thus making it more readily available to the general audience in the field of nonlinear oscillations and nonlinear dynamical systems. Conceivably, this might facilitate getting more people interested in working on this topic. On the other hand, there is always a question as to whether a topic (a) holds enough promise for the future, and (b) has gained enough maturity to be put into book form. With regard to (a), only the future will tell. With regard to (b), I believe that, from the point of view of both foundation and methodology, the methods are far from mature.

Author : Jonathan Borwein,Adrian S. Lewis
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 43,9 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780387312569

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Convex Analysis and Nonlinear Optimization by Jonathan Borwein,Adrian S. Lewis Pdf

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Author : Yoshitsugu Oono
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 45,8 Mb
Release : 2012-10-30
Category : Science
ISBN : 9784431540298

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The Nonlinear World by Yoshitsugu Oono Pdf

The most important characteristic of the “world filled with nonlinearity” is the existence of scale interference: disparate space–time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly. This leads to various peculiar phenomena such as chaos, critical phenomena, and complex biological phenomena, among others. Conceptual analysis and phenomenology are the keys to describe and understand phenomena that are subject to scale interference, because precise description of unfamiliar phenomena requires precise concepts and their phenomenological description. The book starts with an illustration of conceptual analysis in terms of chaos and randomness, and goes on to explain renormalization group philosophy as an approach to phenomenology. Then, abduction is outlined as a way to express what we have understood about the world. The book concludes with discussions on how we can approach genuinely complex phenomena, including biological phenomena. The main target of this volume is young people who have just started to appreciate the world seriously. The author also wishes the book to be helpful to those who have been observing the world, but who wish to appreciate it afresh from a different angle.

Author : Jaime Angulo Pava
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 41,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848975

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Nonlinear Dispersive Equations by Jaime Angulo Pava Pdf

This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.

Author : Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš
Publisher : Springer
Page : 577 pages
File Size : 41,6 Mb
Release : 2019-02-26
Category : Mathematics
ISBN : 9783030034306

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Nonlinear Analysis - Theory and Methods by Nikolaos S. Papageorgiou,Vicenţiu D. Rădulescu,Dušan D. Repovš Pdf

This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.

Author : Mohit Tawarmalani,Nikolaos V. Sahinidis
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 54,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735321

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by Mohit Tawarmalani,Nikolaos V. Sahinidis Pdf

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Author : Stefano Lenci,Giuseppe Rega
Publisher : Springer
Page : 318 pages
File Size : 49,6 Mb
Release : 2018-09-24
Category : Technology & Engineering
ISBN : 9783319997100

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Global Nonlinear Dynamics for Engineering Design and System Safety by Stefano Lenci,Giuseppe Rega Pdf

This is the first book which exploits concepts and tools of global nonlinear dynamics for bridging the gap between theoretical and practical stability of systems/structures, and for possibly enhancing the engineering design in macro-, micro- and nano-mechanics. Addressed topics include complementing theoretical and practical stability to achieve load carrying capacity; dynamical integrity for analyzing global dynamics, for interpreting/predicting experimental behavior, for getting hints towards engineering design; techniques for control of chaos; response of uncontrolled and controlled system/models in applied mechanics and structural dynamics by also considerung the effect of system imperfections; from relatively simple systems to multidimensional models representative of real world applications; potential and expected impact of global dynamics for engineering design.

Author : Antonio Ambrosetti,David Arcoya Álvarez
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 45,5 Mb
Release : 2011-07-19
Category : Mathematics
ISBN : 9780817681142

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An Introduction to Nonlinear Functional Analysis and Elliptic Problems by Antonio Ambrosetti,David Arcoya Álvarez Pdf

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.

Author : Baoxiang Wang,Zhaohui Huo,Chengchun Hao,Zihua Guo
Publisher : World Scientific
Page : 300 pages
File Size : 40,7 Mb
Release : 2011-08-10
Category : Mathematics
ISBN : 9789814458399

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Harmonic Analysis Method for Nonlinear Evolution Equations, I by Baoxiang Wang,Zhaohui Huo,Chengchun Hao,Zihua Guo Pdf

This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein–Gordon equations, KdV equations as well as Navier–Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students. Contents:Fourier Multiplier, Function Spaces Xsp,qNavier–Stokes EquationStrichartz Estimates for Linear Dispersive EquationsLocal and Global Wellposedness for Nonlinear Dispersive EquationsThe Low Regularity Theory for the Nonlinear Dispersive EquationsFrequency-Uniform Decomposition TechniquesConservations, Morawetz' Estimates of Nonlinear Schrödinger EquationsBoltzmann Equation without Angular Cutoff Readership: Graduate students and researchers interested in analysis and PDE. Keywords:Nonlinear Dispersive Equation;Harmonic Analysis MethodKey Features:From PDE point of view, this book gives a self-contained introduction to the theory of function spaces including Besov, modulation and Triebel–Lizorkin spacesThe main topics are concentrated in four kinds of important equations, nonlinear Schrödinger, Navier–Stokes, KdV and Boltzmann equationsThis monograph is a unique treatment of the frequency-uniform localization techniques for nonlinear evolution equationsReviews: "The book under review is well and clearly written and pleasant to read. It is aimed at advanced graduate students; hence, familiarity with basic topics in measure theory, real analysis, complex analysis, functional analysis, etc., is assumed on the part of the reader. Those mathematicians who wish to learn harmonic analysis methods used in PDEs, and who wish to enter into this active area of research, will surely find this book interesting. The book also contains a reasonably large bibliography." Mathematical Reviews