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Nonlinear Theory of Generalized Functions

1999-03-16 Mathematics
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Release : 1999-03-16
Genre : Mathematics
Kind : eBook
Book Rating : 495/5 ( reviews)

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Book Synopsis Nonlinear Theory of Generalized Functions by : Michael Oberguggenberger

Download or read book Nonlinear Theory of Generalized Functions written by Michael Oberguggenberger. This book was released on 1999-03-16. 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.

A Nonlinear Theory of Generalized Functions

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 818/5 ( reviews)

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Book Synopsis A Nonlinear Theory of Generalized Functions by : Hebe de Azevedo Biagioni

Download or read book A Nonlinear Theory of Generalized Functions written by Hebe de Azevedo Biagioni. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.

Introduction to a Nonlinear Theory of Generalized Functions

1988 Nonlinear theories
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Release : 1988
Genre : Nonlinear theories
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Introduction to a Nonlinear Theory of Generalized Functions by : Hebe Azevedo Biagioni

Download or read book Introduction to a Nonlinear Theory of Generalized Functions written by Hebe Azevedo Biagioni. This book was released on 1988. Available in PDF, EPUB and Kindle. Book excerpt:

A Nonlinear Theory of Generalized Functions

1990-03-21 Mathematics
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Release : 1990-03-21
Genre : Mathematics
Kind : eBook
Book Rating : 083/5 ( reviews)

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Book Synopsis A Nonlinear Theory of Generalized Functions by : Hebe de Azevedo Biagioni

Download or read book A Nonlinear Theory of Generalized Functions written by Hebe de Azevedo Biagioni. This book was released on 1990-03-21. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.

Elementary Introduction to New Generalized Functions

2011-08-18 Mathematics
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Release : 2011-08-18
Genre : Mathematics
Kind : eBook
Book Rating : 247/5 ( reviews)

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Book Synopsis Elementary Introduction to New Generalized Functions by : J.F. Colombeau

Download or read book Elementary Introduction to New Generalized Functions written by J.F. Colombeau. This book was released on 2011-08-18. 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.

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