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Multiplication of Distributions

A tool in mathematics, numerical engineering and theoretical physics

  • Book
  • © 1992

Overview

Authors:
  1. Jean François Colombeau
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1532)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction to generalized functions and distributions

    • Jean François Colombeau
    Pages 1-12

  3. Multiplications of distributions in classical physics

    • Jean François Colombeau
    Pages 13-29

  4. Elementary introduction

    • Jean François Colombeau
    Pages 30-61

  5. Jump formulas for systems in nonconservative form. New numerical methods

    • Jean François Colombeau
    Pages 62-96

  6. The case of several constitutive equations

    • Jean François Colombeau
    Pages 97-123

  7. Linear wave propagation in a medium with piecewise C∞ characteristics

    • Jean François Colombeau
    Pages 124-143

  8. The canonical Hamiltonian formalism of interacting quantum fields

    • Jean François Colombeau
    Pages 144-157

  9. The abstract theory of generalized functions

    • Jean François Colombeau
    Pages 158-171

  10. Back Matter

    Pages 172-184
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Keywords

About this book

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).

Bibliographic Information

  • Book Title: Multiplication of Distributions

  • Book Subtitle: A tool in mathematics, numerical engineering and theoretical physics

  • Authors: Jean François Colombeau

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0088952

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1992

  • Softcover ISBN: 978-3-540-56288-7Published: 14 December 1992

  • eBook ISBN: 978-3-540-47510-1Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 186

  • Topics: Applications of Mathematics, Analysis

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