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Regularity Of Difference Equations On Banach Spaces
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Book Synopsis Regularity of Difference Equations on Banach Spaces by : Ravi P. Agarwal
Download or read book Regularity of Difference Equations on Banach Spaces written by Ravi P. Agarwal and published by Springer. This book was released on 2014-06-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
Book Synopsis Differential Equations in Banach Spaces by : Giovanni Dore
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.
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 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
Book Synopsis Path Regularity for Stochastic Differential Equations in Banach Spaces by : Johanna Dettweiler
Download or read book Path Regularity for Stochastic Differential Equations in Banach Spaces written by Johanna Dettweiler and published by . This book was released on 2007 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Differential Equations in Banach Space by : S. G. Kreui
Download or read book Linear Differential Equations in Banach Space written by S. G. Kreui and published by American Mathematical Soc.. This book was released on 2011-07-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations in Banach Spaces by : Angelo Favini
Download or read book Differential Equations in Banach Spaces written by Angelo Favini and published by Lecture Notes in Mathematics. This book was released on 1986-12 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Partial Differential Equations by : Lucio Boccardo
Download or read book Elliptic Partial Differential Equations written by Lucio Boccardo and published by Walter de Gruyter. This book was released on 2013-10-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Book Synopsis Analytic Semigroups and Optimal Regularity in Parabolic Problems by : Alessandra Lunardi
Download or read book Analytic Semigroups and Optimal Regularity in Parabolic Problems written by Alessandra Lunardi and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)
Book Synopsis Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains by : Petru A. Cioica
Download or read book Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains written by Petru A. Cioica and published by Logos Verlag Berlin GmbH. This book was released on 2015-03-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic partial differential equations (SPDEs, for short) are the mathematical models of choice for space time evolutions corrupted by noise. Although in many settings it is known that the resulting SPDEs have a unique solution, in general, this solution is not given explicitly. Thus, in order to make those mathematical models ready to use for real life applications, appropriate numerical algorithms are needed. To increase efficiency, it would be tempting to design suitable adaptive schemes based, e.g., on wavelets. However, it is not a priori clear whether such adaptive strategies can outperform well-established uniform alternatives. Their theoretical justification requires a rigorous regularity analysis in so-called non-linear approximation scales of Besov spaces. In this thesis the regularity of (semi-)linear second order SPDEs of Itô type on general bounded Lipschitz domains is analysed. The non-linear approximation scales of Besov spaces are used to measure the regularity with respect to the space variable, the time regularity being measured first in terms of integrability and afterwards in terms of Hölder norms. In particular, it is shown that in specific situations the spatial Besov regularity of the solution in the non-linear approximation scales is generically higher than its corresponding classical Sobolev regularity. This indicates that it is worth developing spatially adaptive wavelet methods for solving SPDEs instead of using uniform alternatives.
Book Synopsis Difference Equations in Normed Spaces by : Michael Gil
Download or read book Difference Equations in Normed Spaces written by Michael Gil and published by Elsevier. This book was released on 2007-01-08 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete. They also appear in the applications of discretization methods for differential, integral and integro-differential equations. The application of the theory of difference equations is rapidly increasing to various fields, such as numerical analysis, control theory, finite mathematics, and computer sciences. This book is devoted to linear and nonlinear difference equations in a normed space. The main methodology presented in this book is based on a combined use of recent norm estimates for operator-valued functions with the following methods and results: The freezing method The Liapunov type equation The method of majorants The multiplicative representation of solutions Deals systematically with difference equations in normed spaces Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equations Develops the freezing method and presents recent results on Volterra discrete equations Contains an approach based on the estimates for norms of operator functions
Book Synopsis New Difference Schemes for Partial Differential Equations by : Allaberen Ashyralyev
Download or read book New Difference Schemes for Partial Differential Equations written by Allaberen Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.
Book Synopsis Ordinary Differential Equations in Banach Spaces by : K. Deimling
Download or read book Ordinary Differential Equations in Banach Spaces written by K. Deimling and published by Lecture Notes in Mathematics. This book was released on 1977-07 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis in Banach Spaces by : Tuomas Hytönen
Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2016-11-26 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.
Book Synopsis Stability of Nonautonomous Differential Equations by : Luis Barreira
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Book Synopsis New Trends in Difference Equations by : Saber N. Elaydi
Download or read book New Trends in Difference Equations written by Saber N. Elaydi and published by CRC Press. This book was released on 2002-02-28 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series on the International Conference on Difference Equations and Applications has established a tradition within the mathematical community. It brings together scientists from many different areas of research to highlight current interests, challenges and unsolved problems. This volume comprises selected papers presented at the Fifth Interna
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 Variational Analysis of Regular Mappings by : Alexander D. Ioffe
Download or read book Variational Analysis of Regular Mappings written by Alexander D. Ioffe and published by Springer. This book was released on 2017-10-26 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected applications. Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.
