Download or read book Linear Theory of Colombeau Generalized Functions written by M Nedeljkov and published by CRC Press. This book was released on 1998-05-20 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.
Download or read book Multiplication of Distributions written by Jean F. Colombeau and published by Springer. This book was released on 2006-11-15 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Geometric Theory of Generalized Functions with Applications to General Relativity written by M. Grosser and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.
Download or read book Nonlinear Theory of Generalized Functions written by Michael Oberguggenberger and published by Routledge. This book was released on 2022-02-28 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.
Download or read book On the Foundations of Nonlinear Generalized Functions I and II written by Michael Grosser and published by American Mathematical Soc.. This book was released on 2001 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Download or read book Generalized Functions and Their Applications written by R.S. Pathak and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer. This book was released on 2016-12-10 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Download or read book New Generalized Functions and Multiplication of Distributions written by J.F. Colombeau and published by Elsevier. This book was released on 2000-04-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a new mathematical theory of generalized functions, more general than Distribution Theory, giving a rigorous mathematical sense to any product of a finite number of distributions and to heuristic computations of Quantum Field Theory. Although the physical motivations are emphasized, the book is also addressed to mathematicians with no knowledge of physics. This work opens a new domain of research in both pure and applied mathematics.
Download or read book Non Linear Partial Differential Equations written by E.E. Rosinger and published by Elsevier. This book was released on 1990-11-22 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomena have presented increasing difficulties in the mentioned order. In particular, the latter two phenomena necessarily lead to nonclassical or generalized solutions for nonlinear partial differential equations.
Download or read book Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics written by F. Farassat and published by . This book was released on 1994 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin de L Acad mie Serbe Des Sciences Classe Des Sciences Math matiques Et Naturelles written by Srpska akademija nauka i umetnosti and published by . This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elementary Introduction to New Generalized Functions written by J.F. Colombeau and published by Elsevier. This book was released on 2011-08-18 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's previous book `New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced `new generalized functions' in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions. The aim here is to present these functions in a more direct and elementary way. In Part I, the reader is assumed to be familiar only with the concepts of open and compact subsets of R&eegr;, of C∞ functions of several real variables and with some rudiments of integration theory. Part II defines tempered generalized functions, i.e. generalized functions which are, in some sense, increasing at infinity no faster than a polynomial (as well as all their partial derivatives). Part III shows that, in this setting, the partial differential equations have new solutions. The results obtained show that this setting is perfectly adapted to the study of nonlinear partial differential equations, and indicate some new perspectives in this field.
Download or read book Elliptic Operators Topology and Asymptotic Methods written by John Roe and published by CRC Press. This book was released on 2013-12-19 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl
Download or read book Theories of Generalised Functions written by R F Hoskins and published by Elsevier. This book was released on 2005-01-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions. The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins. - Explains and compares the various standard types of generalised functions that have been developed during the 20th Century - Contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions
Download or read book Theory of P adic Distributions written by S. Albeverio and published by Cambridge University Press. This book was released on 2010-03-18 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Download or read book Recent Advances in Modeling Analysis and Systems Control Theoretical Aspects and Applications written by El Hassan Zerrik and published by Springer Nature. This book was released on 2019-08-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent developments in a wide range of areas, including the modeling, analysis and control of dynamical systems, and explores related applications. The book provided a forum where researchers have shared their ideas, results on theory, and experiments in application problems. The current literature devoted to dynamical systems is quite large, and the authors’ choice for the considered topics was motivated by the following considerations. Firstly, the mathematical jargon for systems theory remains quite complex and the authors feel strongly that they have to maintain connections between the people of this research field. Secondly, dynamical systems cover a wider range of applications, including engineering, life sciences and environment. The authors consider that the book is an important contribution to the state of the art in the fuzzy and dynamical systems areas.
