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A Nonlinear Theory of Generalized Functions

  • Book
  • © 1990

Overview

Editors:
  1. Hebe de Azevedo Biagioni
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1421)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-XII
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  2. Generalized functions on an open subset of En

    • Hebe de Azevedo Biagioni
    Pages 1-68

  3. Generalized functions on an arbitrary subset of En

    • Hebe de Azevedo Biagioni
    Pages 69-82

  4. Generalized solutions of nonlinear partial differential equations

    • Hebe de Azevedo Biagioni
    Pages 83-141

  5. Back Matter

    Pages 142-214
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: A Nonlinear Theory of Generalized Functions

  • Editors: Hebe de Azevedo Biagioni

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089552

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-52408-3Published: 21 March 1990

  • eBook ISBN: 978-3-540-46981-0Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 218

  • Topics: Analysis

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