Analysis And Partial Differential Equations

Author : Haim Brezis
Publisher : Springer Science & Business Media
ISBN 13 : 0387709142
Total Pages : 600 pages
Book Rating : 4.47/5 ( download)

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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.

Author : R. M. M. Mattheij
Publisher : SIAM
ISBN 13 : 0898715946
Total Pages : 689 pages
Book Rating : 4.41/5 ( download)

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Download or read book Partial Differential Equations written by R. M. M. Mattheij and published by SIAM. This book was released on 2005-01-01 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.

Author : Davar Khoshnevisan
Publisher : American Mathematical Soc.
ISBN 13 : 147041547X
Total Pages : 127 pages
Book Rating : 4.71/5 ( download)

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Download or read book Analysis of Stochastic Partial Differential Equations written by Davar Khoshnevisan and published by American Mathematical Soc.. This book was released on 2014-06-11 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.

Author : Iorio Júnior Iorio Jr.
Publisher : Cambridge University Press
ISBN 13 : 9780521621168
Total Pages : 428 pages
Book Rating : 4.6X/5 ( download)

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Download or read book Fourier Analysis and Partial Differential Equations written by Iorio Júnior Iorio Jr. and published by Cambridge University Press. This book was released on 2001-03-15 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.

Author : A. M. Vinogradov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897997
Total Pages : 268 pages
Book Rating : 4.93/5 ( download)

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Download or read book Cohomological Analysis of Partial Differential Equations and Secondary Calculus written by A. M. Vinogradov and published by American Mathematical Soc.. This book was released on 2001-10-16 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182 in this same series, Translations of Mathematical Monographs, and shows the theory "in action".

Author : S. H, Lui
Publisher : John Wiley & Sons
ISBN 13 : 0470647280
Total Pages : 506 pages
Book Rating : 4.88/5 ( download)

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Download or read book Numerical Analysis of Partial Differential Equations written by S. H, Lui and published by John Wiley & Sons. This book was released on 2011-08-30 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Author : Franco Brezzi
Publisher : Springer Science & Business Media
ISBN 13 : 8847025923
Total Pages : 394 pages
Book Rating : 4.29/5 ( download)

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Download or read book Analysis and Numerics of Partial Differential Equations written by Franco Brezzi and published by Springer Science & Business Media. This book was released on 2012-12-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.

Author : Graham Griffiths
Publisher : Academic Press
ISBN 13 : 9780123846532
Total Pages : 461 pages
Book Rating : 4.36/5 ( download)

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Download or read book Traveling Wave Analysis of Partial Differential Equations written by Graham Griffiths and published by Academic Press. This book was released on 2010-12-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net Includes a spectrum of applications in science, engineering, applied mathematics Presents a combination of numerical and analytical methods Provides transportable computer codes in Matlab and Maple

Author : Nakhlé H. Asmar
Publisher :
ISBN 13 :
Total Pages : 904 pages
Book Rating : 4.68/5 ( download)

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Download or read book Applied Complex Analysis with Partial Differential Equations written by Nakhlé H. Asmar and published by . This book was released on 2002 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource. Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates. For engineers and physicists in need of a quick reference tool.

Author : V. Hutson
Publisher : Elsevier
ISBN 13 : 0080527310
Total Pages : 442 pages
Book Rating : 4.14/5 ( download)

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Download or read book Applications of Functional Analysis and Operator Theory written by V. Hutson and published by Elsevier. This book was released on 2005-02-08 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results Introduces each new topic with a clear, concise explanation Includes numerous examples linking fundamental principles with applications Solidifies the reader's understanding with numerous end-of-chapter problems