Download or read book Differential Operators for Partial Differential Equations and Function Theoretic Applications written by K. W. Bauer and published by Springer. This book was released on 2007-02-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Operator Theory and Differential Equations written by Anatoly G. Kusraev and published by Springer Nature. This book was released on 2021-01-13 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019. Intended for mathematicians specializing in operator theory, functional spaces, differential equations or mathematical modeling, the book provides a state-of-the-art account of various fascinating areas of operator theory, ranging from various classes of operators (positive operators, convolution operators, backward shift operators, singular and fractional integral operators, partial differential operators) to important applications in differential equations, inverse problems, approximation theory, metric theory of surfaces, the Hubbard model, social stratification models, and viscid incompressible fluids.
Download or read book The Analysis of Linear Partial Differential Operators I written by Lars Hörmander and published by Springer. This book was released on 1990-08-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.
Download or read book Semigroups of Linear Operators and Applications to Partial Differential Equations written by Amnon Pazy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.
Download or read book Fundamental Solutions for Differential Operators and Applications written by Prem Kythe and published by Springer Science & Business Media. This book was released on 1996-07-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators, and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects.
Download or read book Pseudo Differential Operators Complex Analysis and Partial Differential Equations written by Bert-Wolfgang Schulze and published by Springer Science & Business Media. This book was released on 2010-03-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.
Download or read book Distributions Partial Differential Equations and Harmonic Analysis written by Dorina Mitrea and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.
Download or read book Carleman Estimates for Second Order Partial Differential Operators and Applications written by Xiaoyu Fu and published by Springer Nature. This book was released on 2019-10-31 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
Download or read book Partial Differential Equations written by András Vasy and published by American Mathematical Soc.. This book was released on 2015-12-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the features one wants without the overhead of measure theory. There is additional material provided for readers who would like to learn more than the core material, and there are numerous exercises to help solidify one's understanding. The text should be suitable for advanced undergraduates or for beginning graduate students including those in engineering or the sciences.
Download or read book Green s Functions and Linear Differential Equations written by Prem K. Kythe and published by CRC Press. This book was released on 2011-01-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Green's Functions and Linear Differential Equations: Theory, Applications, and Computation presents a variety of methods to solve linear ordinary differential equations (ODEs) and partial differential equations (PDEs). The text provides a sufficient theoretical basis to understand Green's function method, which is used to solve initial and boundary
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Download or read book Elliptic Functional Differential Equations and Applications written by Alexander L. Skubachevskii and published by Birkhäuser. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved only in some subdomains. The symbol of a self-adjoint semibounded functional differential operator can change its sign. The purpose of this book is to present for the first time general results concerning solvability and spectrum of these problems, a priori estimates and smoothness of solutions. The approach is based on the properties of elliptic operators and difference operators in Sobolev spaces. The most important features distinguishing this work are applications to different fields of science. The methods in this book are used to obtain new results regarding the solvability of nonlocal elliptic boundary value problems and the existence of Feller semigroups for multidimensional diffusion processes. Moreover, applications to control theory and aircraft and rocket technology are given. The theory is illustrated with numerous figures and examples. The book is addresssed to graduate students and researchers in partial differential equations and functional differential equations. It will also be of use to engineers in control theory and elasticity theory.
Download or read book The Analysis of Linear Partial Differential Operators III written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 2007-03-15 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987. "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.
Download or read book Nonlinear Evolution Operators and Semigroups written by Nicolae H. Pavel and published by . This book was released on 2014-01-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Differential Operators written by Cornelius Lanczos and published by SIAM. This book was released on 1997-12-01 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1961, this Classics edition continues to be appealing because it describes a large number of techniques still useful today. Although the primary focus is on the analytical theory, concrete cases are cited to forge the link between theory and practice. Considerable manipulative skill in the practice of differential equations is to be developed by solving the 350 problems in the text. The problems are intended as stimulating corollaries linking theory with application and providing the reader with the foundation for tackling more difficult problems. Lanczos begins with three introductory chapters that explore some of the technical tools needed later in the book, and then goes on to discuss interpolation, harmonic analysis, matrix calculus, the concept of the function space, boundary value problems, and the numerical solution of trajectory problems, among other things. The emphasis is constantly on one question: "What are the basic and characteristic properties of linear differential operators?" In the author's words, this book is written for those "to whom a problem in ordinary or partial differential equations is not a problem of logical acrobatism, but a problem in the exploration of the physical universe. To get an explicit solution of a given boundary value problem is in this age of large electronic computers no longer a basic question. But of what value is the numerical answer if the scientist does not understand the peculiar analytical properties and idiosyncrasies of the given operator? The author hopes that this book will help in this task by telling something about the manifold aspects of a fascinating field."
