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Nonlinear Differential Equations Of Monotone Types In Banach Spaces


Nonlinear Differential Equations Of Monotone Types In Banach Spaces
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Nonlinear Differential Equations Of Monotone Types In Banach Spaces


Nonlinear Differential Equations Of Monotone Types In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01

Nonlinear Differential Equations Of Monotone Types In Banach Spaces written by Viorel Barbu 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 2010-01-01 with Mathematics categories.


This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.



Nonlinear Differential Equations Of Monotone Types In Banach Spaces


Nonlinear Differential Equations Of Monotone Types In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer
Release Date : 2010

Nonlinear Differential Equations Of Monotone Types In Banach Spaces written by Viorel Barbu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Banach spaces categories.


This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. This is a monograph about the most significant results obtained in this area in last decades but is also written as a graduate textbook on modern methods in partial differential equations with main emphasis on applications to fundamental mathematical models of mathematical physics, fluid dynamics and mechanics. This book is selfcontained while the prerequisites in functional analysis are necessary to unde.



Monotone Operators In Banach Space And Nonlinear Partial Differential Equations


Monotone Operators In Banach Space And Nonlinear Partial Differential Equations
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Author : R. E. Showalter
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-22

Monotone Operators In Banach Space And Nonlinear Partial Differential Equations written by R. E. Showalter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-22 with Mathematics categories.


The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.



Nonlinear Ill Posed Problems Of Monotone Type


Nonlinear Ill Posed Problems Of Monotone Type
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Author : Yakov Alber
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-02

Nonlinear Ill Posed Problems Of Monotone Type written by Yakov Alber 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 2006-02-02 with Mathematics categories.


Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.



Convexity And Optimization In Banach Spaces


Convexity And Optimization In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-03

Convexity And Optimization In Banach Spaces written by Viorel Barbu 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 2012-01-03 with Mathematics categories.


An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.



Nonlinear Partial Differential Equations With Applications


Nonlinear Partial Differential Equations With Applications
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Author : Tomáš Roubíček
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13

Nonlinear Partial Differential Equations With Applications written by Tomáš Roubíček 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 2013-01-13 with Mathematics categories.


This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook. The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems. ------ The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (...) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world. (Mathematical Reviews)



Functional Analysis And The Feynman Operator Calculus


Functional Analysis And The Feynman Operator Calculus
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Author : Tepper Gill
language : en
Publisher: Springer
Release Date : 2016-03-30

Functional Analysis And The Feynman Operator Calculus written by Tepper Gill and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.


This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.



Topological And Variational Methods With Applications To Nonlinear Boundary Value Problems


Topological And Variational Methods With Applications To Nonlinear Boundary Value Problems
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Author : Dumitru Motreanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19

Topological And Variational Methods With Applications To Nonlinear 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 2013-11-19 with Mathematics categories.


This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.



Stabilization Of Distributed Parameter Systems Design Methods And Applications


Stabilization Of Distributed Parameter Systems Design Methods And Applications
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Author : Grigory Sklyar
language : en
Publisher: Springer Nature
Release Date : 2021-03-01

Stabilization Of Distributed Parameter Systems Design Methods And Applications written by Grigory Sklyar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-01 with Science categories.


This book presents recent results and envisages new solutions of the stabilization problem for infinite-dimensional control systems. Its content is based on the extended versions of presentations at the Thematic Minisymposium “Stabilization of Distributed Parameter Systems: Design Methods and Applications” at ICIAM 2019, held in Valencia from 15 to 19 July 2019. This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces. This includes new results in the theory of nonlinear semigroups, port-Hamiltonian systems, turnpike phenomenon, and further developments of Lyapunov's direct method. The scope of the book also covers applications of these methods to mathematical models in continuum mechanics and chemical engineering. It is addressed to readers interested in control theory, differential equations, and dynamical systems.