Nonlinear Semigroups And Differential Equations In Banach Spaces
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Nonlinear Semigroups And Differential Equations In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer
Release Date : 1976-04-06
Nonlinear Semigroups And Differential Equations 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 1976-04-06 with Mathematics categories.
This book is concerned with nonlinear semigroups of contractions in Banach spaces and their application to the existence theory for differential equa tions associated with nonlinear dissipative operators. The study of nonlinear semi groups resulted from the examination of nonlinear parabolic equations and from various nonlinear boundary value problems. The first work done by Y. Komura stimulated much further work and interest in this subject. Thus a series of studies was begun and then continued by T. Kato, M. G. Crandall, A. Pazy, H. Brezis and others, who made important con tributions to the development of the theory. The theory as developed below is a generalisation of the Hille-Yosida theory for one-parameter semigroups of linear operators and is a collection of diversified results unified more or less loosely by their methods of approach. This theory is also closely related to the theory of nonlinear monotone operators. Of course not all aspects of this theory could be covered in our expo sition, and many important contributions to the subject have been excluded for the sake of brevity. We have attempted to present the basic results to the reader and to orient him toward some of the applications. This book is intended to be self-contained. The reader is assumed to have only a basic knowledge of functional analysis, function theory and partial differential equations. Some of the necessary prerequisites for the reading of this 'book are summarized, with or without proof, in Chapter I.
Nonlinear Semigroups And Differential Equations In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer
Release Date : 1976-04-15
Nonlinear Semigroups And Differential Equations 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 1976-04-15 with Mathematics categories.
This book is concerned with nonlinear semigroups of contractions in Banach spaces and their application to the existence theory for differential equa tions associated with nonlinear dissipative operators. The study of nonlinear semi groups resulted from the examination of nonlinear parabolic equations and from various nonlinear boundary value problems. The first work done by Y. Komura stimulated much further work and interest in this subject. Thus a series of studies was begun and then continued by T. Kato, M. G. Crandall, A. Pazy, H. Brezis and others, who made important con tributions to the development of the theory. The theory as developed below is a generalisation of the Hille-Yosida theory for one-parameter semigroups of linear operators and is a collection of diversified results unified more or less loosely by their methods of approach. This theory is also closely related to the theory of nonlinear monotone operators. Of course not all aspects of this theory could be covered in our expo sition, and many important contributions to the subject have been excluded for the sake of brevity. We have attempted to present the basic results to the reader and to orient him toward some of the applications. This book is intended to be self-contained. The reader is assumed to have only a basic knowledge of functional analysis, function theory and partial differential equations. Some of the necessary prerequisites for the reading of this 'book are summarized, with or without proof, in Chapter I.
Differential Equations In Banach Spaces
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Author : Giovanni Dore
language : en
Publisher: CRC Press
Release Date : 2020-10-07
Differential Equations In Banach Spaces written by Giovanni Dore and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.
This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.
Nonlinear Semigroups
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Author : Isao Miyadera
language : en
Publisher: American Mathematical Soc.
Release Date :
Nonlinear Semigroups written by Isao Miyadera 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 with Mathematics categories.
This book presents a systematic exposition of the general theory of nonlinear contraction semigroups in Banach spaces and is aimed at students and researchers in science and engineering as well as in mathematics. Suitable for use as a textbook in graduate courses and seminars, this self-contained book is accessible to those with only a basic knowledge of functional analysis. After preprequisites presented in the first chapter, Miyadera covers the basic properties of dissipative operators and nonlinear contraction semigroups in Banach spaces. The generation of nonlinear contraction semigroups, the Komura theorem, and the Crandall-Liggett theorem are explored, and there is a treatment of the convergence of difference approximation of Cauchy problems for ????- dissipative operators and the Kobayashi generation theorem of nonlinear semigroups. Nonlinear Semigroups concludes with applications to nonlinear evolution equations and to first order quasilinear equations.
Nonlinear Operators And Differential Equations In Banach Spaces
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Author : Robert H. Martin
language : en
Publisher:
Release Date : 1987
Nonlinear Operators And Differential Equations In Banach Spaces written by Robert H. Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Banach Spaces categories.
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 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 Functional Evolutions In Banach Spaces
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Author : Ki Sik Ha
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Nonlinear Functional Evolutions In Banach Spaces written by Ki Sik Ha 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 2013-04-17 with Mathematics categories.
There are many problems in nonlinear partial differential equations with delay which arise from, for example, physical models, biochemical models, and social models. Some of them can be formulated as nonlinear functional evolutions in infinite-dimensional abstract spaces. Since Webb (1976) considered autonomous nonlinear functional evo lutions in infinite-dimensional real Hilbert spaces, many nonlinear an alysts have studied for the last nearly three decades autonomous non linear functional evolutions, non-autonomous nonlinear functional evo lutions and quasi-nonlinear functional evolutions in infinite-dimensional real Banach spaces. The techniques developed for nonlinear evolutions in infinite-dimensional real Banach spaces are applied. This book gives a detailed account of the recent state of theory of nonlinear functional evolutions associated with accretive operators in infinite-dimensional real Banach spaces. Existence, uniqueness, and stability for 'solutions' of nonlinear func tional evolutions are considered. Solutions are presented by nonlinear semigroups, or evolution operators, or methods of lines, or inequalities by Benilan. This book is divided into four chapters. Chapter 1 contains some basic concepts and results in the theory of nonlinear operators and nonlinear evolutions in real Banach spaces, that play very important roles in the following three chapters. Chapter 2 deals with autonomous nonlinear functional evolutions in infinite-dimensional real Banach spaces. Chapter 3 is devoted to non-autonomous nonlinear functional evolu tions in infinite-dimensional real Banach spaces. Finally, in Chapter 4 quasi-nonlinear functional evolutions are con sidered in infinite-dimensional real Banach spaces.
Semigroup Approach To Nonlinear Diffusion Equations
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Author : Viorel Barbu
language : en
Publisher: World Scientific
Release Date : 2021-09-23
Semigroup Approach To Nonlinear Diffusion Equations written by Viorel Barbu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.
This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.
Degenerate Differential Equations In Banach Spaces
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Author : Angelo Favini
language : en
Publisher: CRC Press
Release Date : 1998-09-10
Degenerate Differential Equations In Banach Spaces written by Angelo Favini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-10 with Mathematics categories.
This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.