Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces PDF Download
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Author: Felix E. Browder
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Author: Felix E. Browder
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Author: Songmu Zheng
Publisher: Chapman and Hall/CRC
ISBN: 9781584884521
Category : Mathematics
Languages : en
Pages : 304
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Book Description
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator methods, the monotone iterative method and invariant regions, the global existence and uniqueness theory for small initial data, and the asymptotic behavior of solutions and global attractors. Many of the results are published in book form for the first time. Bibliographic comments in each chapter provide the reader with references and further reading materials to enable further research and study.
Author: Reinhard Racke
Publisher: Birkhäuser
ISBN: 9783319218724
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
Author: J. Kral
Publisher: Springer
ISBN: 9780306308352
Category : Mathematics
Languages : en
Pages : 146
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Book Description
Autoři věnují pozornost různým problémům teorie potenciálu, na něž aplikují diferenciální rovnice určitých typů. Problematiku shrnují pod názvem nelineární rovnice evoluční. V četných případech vystupuje parabolický typ
Author: N. U. Ahmed
Publisher: Springer Nature
ISBN: 3031372603
Category : Mathematics
Languages : en
Pages : 236
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Book Description
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.
Author: Felix E. Browder
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Ki Sik Ha
Publisher: Springer Science & Business Media
ISBN: 9781402010910
Category : Mathematics
Languages : en
Pages : 92
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Book Description
There are many problems in partial differential equations with delay which arise from physical models with delay, biochemical models with delay and diffused population with delay. Some of them can be considered as nonlinear functional evolutions in appropriate infinite dimensional spaces. While other publications in the same field have treated linear functional evolutions and nonlinear functional evolutions in finite dimensional spaces, this book is one of the first to give a detailed account of the recent state of the theory of nonlinear functional evolutions associated with multi-valued operators in infinite dimensional real Banach spaces. The techniques developed for nonlinear evolutions in real Banach spaces are applied in this book. This book will benefit graduate students and researchers working in such diverse fields as mathematics, physics, biochemistry, and sociology who are interested in the development and application of nonlinear functional evolutions. This volume will also be useful as supplementary reading for biologists and engineers.
Author: Nicolae H. Pavel
Publisher: Springer
ISBN: 3540471863
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Behzad Djafari-Rouhani
Publisher: CRC Press
ISBN: 9780367780128
Category : Differential equations
Languages : en
Pages : 240
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Book Description
This book deals with first and second order evolution and difference monotone type equations. The approach followed in the book was first introduced by Dr. Djafari-Rouhani, and later advanced by him along with Dr. Khatibzadeh.
