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Monotone Operators In Banach Space And Nonlinear Partial Differential Equations
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Book Synopsis Monotone Operators in Banach Space and Nonlinear Partial Differential Equations by : R. E. Showalter
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.
Book Synopsis Monotone Operators in Banach Space and Nonlinear Partial Differential Equations by :
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:
Book Synopsis Nonlinear Differential Equations of Monotone Types in Banach Spaces by : Viorel Barbu
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.
Book Synopsis Nonlinear Semigroups and Differential Equations in Banach Spaces by : Viorel Barbu
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.
Book Synopsis Nonlinear Ill-posed Problems of Monotone Type by : Yakov Alber
Download or read book Nonlinear Ill-posed Problems of Monotone Type written by Yakov Alber and published by Springer Science & Business Media. This book was released on 2006-02-23 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Analysis by : Erich H. Rothe
Download or read book Nonlinear Analysis written by Erich H. Rothe and published by Academic Press. This book was released on 2014-05-10 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe is a collection of papers in honor of Erich H. Rothe, a mathematician who has made significant contributions to various aspects of nonlinear functional analysis. Topics covered range from periodic solutions of semilinear parabolic equations to nonlinear problems across a point of resonance for non-self-adjoint systems. Nonlinear boundary value problems for ordinary differential equations are also considered. Comprised of 14 chapters, this volume first discusses the use of fixed-point theorems in ordered Banach spaces to prove existence and multiplicity result for periodic solutions of semilinear parabolic differential equations of the second order. The reader is then introduced to linear maximal monotone operators and singular nonlinear integral equations of Hammerstein type. Subsequent chapters focus on the branching of periodic solutions of non-autonomous systems; restricted generic bifurcation; Tikhonov regularization and nonlinear problems at resonance; and minimax theorems and their applications to nonlinear partial differential equations. This monograph will be of interest to students and practitioners in the field of mathematics.
Book Synopsis Nonlinear Partial Differential Equations by : A Benkirane
Download or read book Nonlinear Partial Differential Equations written by A Benkirane and published by CRC Press. This book was released on 1996-04-11 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of selected contributions on recent results in nonlinear partial differential equations from participants to an international conference held in Fes, Morocco in 1994. The emphasis is on nonlinear elliptic boundary value problems, but there are also papers deveoted to related areas such as monotone operator theory, calculus of variations, Hamiltonian systems and periodic solutions. Some of the papers are exhaustive surveys, while others contain new results,published here for the first time. This book will be of particular interest to graduate or postgraduate students as well as to specialists in these areas.
Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis
Download or read book Functional Analysis, Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Book Synopsis Theory and Applications of Nonlinear Operators of Accretive and Monotone Type by : Athanass Kartsatos
Download or read book Theory and Applications of Nonlinear Operators of Accretive and Monotone Type written by Athanass Kartsatos and published by CRC Press. This book was released on 1996-03-14 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.
Book Synopsis Nonlinear Functional Analysis and its Applications by : E. Zeidler
Download or read book Nonlinear Functional Analysis and its Applications written by E. Zeidler and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.
Book Synopsis Nonlinear semigroups and differential equations in Banach spaces by : Viorel Barbu
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.
Book Synopsis Current Research in Nonlinear Analysis by : Themistocles M. Rassias
Download or read book Current Research in Nonlinear Analysis written by Themistocles M. Rassias and published by Springer. This book was released on 2018-06-18 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader’s understanding of theories, methods, and techniques utilized to solve significant problems. Topics include: Sobolev Spaces Maximal monotone operators A theorem of Brezis-Nirenberg Operator-norm convergence of the Trotter product formula Elliptic operators with infinitely many variables Pseudo-and quasiconvexities for nonsmooth function Anisotropic surface measures Eulerian and Lagrangian variables Multiple periodic solutions of Lagrangian systems Porous medium equation Nondiscrete Lassonde-Revalski principle Graduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg’s fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field.
Book Synopsis Variational Methods in Nonlinear Analysis by : Dimitrios C. Kravvaritis
Download or read book Variational Methods in Nonlinear Analysis written by Dimitrios C. Kravvaritis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-04-06 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.
Book Synopsis Nonlinear Evolution Operators and Semigroups by : Nicolae H. Pavel
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.
Book Synopsis Nonlinear Systems of Partial Differential Equations by :
Download or read book Nonlinear Systems of Partial Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Theory of Maximal Monotone Operators by : Rangachary Kannan
Download or read book Introduction to the Theory of Maximal Monotone Operators written by Rangachary Kannan and published by . This book was released on 1973 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Degenerate Differential Equations in Banach Spaces by : Angelo Favini
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 338 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 analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.
