Multiplication of Distributions and Applications to Partial Differential Equations
Author: Michael Oberguggenberger
Publisher:
Published: 1992
Total Pages: 330
ISBN-13: 9780608052304
DOWNLOAD EBOOK →Author: Michael Oberguggenberger
Publisher:
Published: 1992
Total Pages: 330
ISBN-13: 9780608052304
DOWNLOAD EBOOK →Author: Michael Oberguggenberger
Publisher: Longman Sc & Tech
Published: 1992
Total Pages: 312
ISBN-13: 9780470219737
DOWNLOAD EBOOK →Author: C. Zuily
Publisher: Elsevier
Published: 1988-04-01
Total Pages: 247
ISBN-13: 0080872549
DOWNLOAD EBOOK →The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.
Author: Robert S Strichartz
Publisher: World Scientific Publishing Company
Published: 2003-06-13
Total Pages: 238
ISBN-13: 9813102292
DOWNLOAD EBOOK →This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Author: J.J. Duistermaat
Publisher: Springer Science & Business Media
Published: 2010-08-09
Total Pages: 455
ISBN-13: 0817646752
DOWNLOAD EBOOK →This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Author: Elemer E. Rosinger
Publisher: Springer
Published: 2006-11-15
Total Pages: 155
ISBN-13: 3540357076
DOWNLOAD EBOOK →Author: Abdellah El Kinani
Publisher: World Scientific
Published: 2010
Total Pages: 219
ISBN-13: 9814304921
DOWNLOAD EBOOK →The general frame for the resolution of PDEs is the theory of kernels ù the first elements of which are sufficient to show the practicality of distribution theory in applications. --
Author: Jean F. Colombeau
Publisher: Springer
Published: 2006-11-15
Total Pages: 193
ISBN-13: 3540475109
DOWNLOAD EBOOK →This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).
Author: Adina Chirilă
Publisher: Springer Nature
Published: 2021-02-08
Total Pages: 277
ISBN-13: 3030671593
DOWNLOAD EBOOK →This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method. The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.
Author: A.H. Zemanian
Publisher: Courier Corporation
Published: 2011-11-30
Total Pages: 400
ISBN-13: 0486151948
DOWNLOAD EBOOK →Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.