Fourier Analysis And Nonlinear Partial Differential Equations PDF Download
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| Author | : Hajer Bahouri |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 530 |
| Release | : 2011-01-03 |
| Genre | : Mathematics |
| ISBN | : 3642168302 |
Download Fourier Analysis and Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
| Author | : Jose Garcia-Cuerva |
| Publisher | : CRC Press |
| Total Pages | : 336 |
| Release | : 2018-01-18 |
| Genre | : Mathematics |
| ISBN | : 135108058X |
Download Fourier Analysis and Partial Differential Equations Book in PDF, ePub and Kindle
Contains easy access to four actual and active areas of research in Fourier Analysis and PDE Covers a wide spectrum of topics in present research Provides a complete picture of state-of-the-art methods in the field Contains 200 tables allowing the reader speedy access to precise data
| Author | : Iorio Júnior Iorio Jr. |
| Publisher | : Cambridge University Press |
| Total Pages | : 428 |
| Release | : 2001-03-15 |
| Genre | : Mathematics |
| ISBN | : 9780521621168 |
Download Fourier Analysis and Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Victor Shapiro |
| Publisher | : CRC Press |
| Total Pages | : 352 |
| Release | : 2011-03-28 |
| Genre | : Mathematics |
| ISBN | : 1439854289 |
Download Fourier Series in Several Variables with Applications to Partial Differential Equations Book in PDF, ePub and Kindle
Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (PDEs). Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear e
| Author | : Lokenath Debnath |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 602 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1489928464 |
Download Nonlinear Partial Differential Equations for Scientists and Engineers Book in PDF, ePub and Kindle
This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.
| Author | : Felipe Linares |
| Publisher | : Springer |
| Total Pages | : 308 |
| Release | : 2014-12-15 |
| Genre | : Mathematics |
| ISBN | : 1493921819 |
Download Introduction to Nonlinear Dispersive Equations Book in PDF, ePub and Kindle
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.
| Author | : Michael Ruzhansky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 416 |
| Release | : 2014-01-18 |
| Genre | : Mathematics |
| ISBN | : 3319025503 |
Download Fourier Analysis Book in PDF, ePub and Kindle
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
| Author | : Peter J Costa |
| Publisher | : Springer Nature |
| Total Pages | : 228 |
| Release | : 2022-06-01 |
| Genre | : Mathematics |
| ISBN | : 3031024346 |
Download Select Ideas in Partial Differential Equations Book in PDF, ePub and Kindle
This text provides an introduction to the applications and implementations of partial differential equations. The content is structured in three progressive levels which are suited for upper–level undergraduates with background in multivariable calculus and elementary linear algebra (chapters 1–5), first– and second–year graduate students who have taken advanced calculus and real analysis (chapters 6-7), as well as doctoral-level students with an understanding of linear and nonlinear functional analysis (chapters 7-8) respectively. Level one gives readers a full exposure to the fundamental linear partial differential equations of physics. It details methods to understand and solve these equations leading ultimately to solutions of Maxwell’s equations. Level two addresses nonlinearity and provides examples of separation of variables, linearizing change of variables, and the inverse scattering transform for select nonlinear partial differential equations. Level three presents rich sources of advanced techniques and strategies for the study of nonlinear partial differential equations, including unique and previously unpublished results. Ultimately the text aims to familiarize readers in applied mathematics, physics, and engineering with some of the myriad techniques that have been developed to model and solve linear and nonlinear partial differential equations.
| Author | : M. W. Wong |
| Publisher | : CRC Press |
| Total Pages | : 208 |
| Release | : 2022-08-19 |
| Genre | : Mathematics |
| ISBN | : 1000636801 |
Download Partial Differential Equations Book in PDF, ePub and Kindle
Partial Differential Equations: Topics in Fourier Analysis, Second Edition explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It shows how this powerful approach is valuable in getting plausible answers that can then be justified by modern analysis. Using Fourier analysis, the text constructs explicit formulas for solving PDEs governed by canonical operators related to the Laplacian on the Euclidean space. After presenting background material, it focuses on: Second-order equations governed by the Laplacian on Rn; the Hermite operator and corresponding equation; and the sub-Laplacian on the Heisenberg group Designed for a one-semester course, this text provides a bridge between the standard PDE course for undergraduate students in science and engineering and the PDE course for graduate students in mathematics who are pursuing a research career in analysis. Through its coverage of fundamental examples of PDEs, the book prepares students for studying more advanced topics such as pseudo-differential operators. It also helps them appreciate PDEs as beautiful structures in analysis, rather than a bunch of isolated ad-hoc techniques. New to the Second Edition Three brand new chapters covering several topics in analysis not explored in the first edition Complete revision of the text to correct errors, remove redundancies, and update outdated material Expanded references and bibliography New and revised exercises.
| Author | : Ravi P. Agarwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 422 |
| Release | : 2008-11-13 |
| Genre | : Mathematics |
| ISBN | : 0387791469 |
Download Ordinary and Partial Differential Equations Book in PDF, ePub and Kindle
In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
