Download or read book Nonlinear Semigroups and Differential Equations in Banach Spaces written by Viorel Barbu and published by Springer. This book was released on 1976-04-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Differential Equations of Monotone Types in Banach Spaces written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear semigroups and differential equations in Banach spaces written by Viorel Barbu and published by Springer. This book was released on 1976-04-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Semigroups written by Isao Miyadera and published by American Mathematical Soc.. This book was released on with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Equations in Banach Spaces written by Giovanni Dore and published by CRC Press. This book was released on 2020-10-07 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Operators and Differential Equations in Banach Spaces written by Robert H. Martin and published by . This book was released on 1987 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monotone Operators in Banach Space and Nonlinear Partial Differential Equations written by R. E. Showalter and published by American Mathematical Soc.. This book was released on 2013-02-22 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Semigroups Fixed Points and Geometry of Domains in Banach Spaces written by Simeon Reich and published by Imperial College Press. This book was released on 2005 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments.
Download or read book Nonlinear Functional Evolutions in Banach Spaces written by Ki Sik Ha and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Semigroups Partial Differential Equations and Attractors written by T.L. Gill and published by Springer. This book was released on 2006-11-15 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It soon became clear, however, that the dynamical systems approach interfaced significantly with many important branches of applied mathematics. As a consequence, the scope of this resulting proceedings volume is an enlarged one with coverage of a wider range of research topics.
Download or read book Semigroup Approach To Nonlinear Diffusion Equations written by Viorel Barbu and published by World Scientific. This book was released on 2021-09-23 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Degenerate Differential Equations in Banach Spaces written by Angelo Favini and published by CRC Press. This book was released on 1998-09-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 an
Download or read book Semigroup Theory and Evolution Equations written by Philippe Clement and published by CRC Press. This book was released on 1991-06-24 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Second International Conference on Trends in Semigroup Theory and Evolution Equations held Sept. 1989, Delft University of Technology, the Netherlands. Papers deal with recent developments in semigroup theory (e.g., positive, dual, integrated), and nonlinear evolution equations (e
Download or read book Nonlinear Semigroups Partial Differential Equations and Attractors written by Tepper L. Gill and published by Springer. This book was released on 2006-11-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Evolution Operators and Semigroups written by Nicolae H. Pavel and published by Springer. This book was released on 2006-11-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Almost Periodic Solutions of Differential Equations in Banach Spaces written by Yoshiyuki Hino and published by CRC Press. This book was released on 2001-10-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with
Download or read book Monotone Operators in Banach Space and Nonlinear Partial Differential Equations written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
