Differential Operators for Partial Differential Equations and Function Theoretic Applications
Author: K. W. Bauer
Publisher: Springer
Published: 2007-02-08
Total Pages: 264
ISBN-13: 3540392114
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Operator Theory and Differential Equations
Author: Anatoly G. Kusraev
Publisher: Springer Nature
Published: 2021-01-13
Total Pages: 337
ISBN-13: 3030497631
DOWNLOAD EBOOKThis 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.
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Author: Haim Brezis
Publisher: Springer Science & Business Media
Published: 2010-11-02
Total Pages: 600
ISBN-13: 0387709142
DOWNLOAD EBOOKThis 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.
The Analysis of Linear Partial Differential Operators I
Author: Lars Hörmander
Publisher: Springer
Published: 1990-08-10
Total Pages: 462
ISBN-13: 9783540523437
DOWNLOAD EBOOKThe 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.
Semigroups of Linear Operators and Applications to Partial Differential Equations
Author: Amnon Pazy
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 289
ISBN-13: 1461255619
DOWNLOAD EBOOKSince 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.
Fundamental Solutions for Differential Operators and Applications
Author: Prem Kythe
Publisher: Springer Science & Business Media
Published: 1996-07-30
Total Pages: 448
ISBN-13: 9780817638696
DOWNLOAD EBOOKA 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.
Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations
Author: Bert-Wolfgang Schulze
Publisher: Springer Science & Business Media
Published: 2010-03-01
Total Pages: 294
ISBN-13: 3034601980
DOWNLOAD EBOOKConsists 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.
Distributions, Partial Differential Equations, and Harmonic Analysis
Author: Dorina Mitrea
Publisher: Springer Science & Business Media
Published: 2013-09-20
Total Pages: 475
ISBN-13: 1461482089
DOWNLOAD EBOOKThe 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.
Carleman Estimates for Second Order Partial Differential Operators and Applications
Author: Xiaoyu Fu
Publisher: Springer Nature
Published: 2019-10-31
Total Pages: 136
ISBN-13: 3030295303
DOWNLOAD EBOOKThis 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.
Partial Differential Equations
Author: András Vasy
Publisher: American Mathematical Soc.
Published: 2015-12-21
Total Pages: 295
ISBN-13: 1470418819
DOWNLOAD EBOOKThis 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.
