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Generalized Functions; Multiplication of Distributions; Applications to Elasticity, Elastoplasticity, Fluid Dynamics and Acoustics

  • Chapter
Generalized Functions, Convergence Structures, and Their Applications

Abstract

If Ω denotes any open set in ℝn, I have defined an algebra G (Ω) of “generalized functions” on Ω. One has the set of inclusions

$${\text{C}}^\infty \left( \Omega \right) \subset D\prime \left( \Omega \right) \subset G\left( \Omega \right)$$

where C∞ (Ω) (respectively D’ (Ω) denotes the set of all C∞ functions (resp. all distributions) on Ω. Two basic points have to be stressed:

  • C∞ (Ω), with its usual pointwise multiplication, is a subalgebra of G(Ω)

  • any element of G(Ω) admits partial derivatives of any order which generalize exactly those in D’ (Ω).

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Author information

Authors and Affiliations

  1. U.E.R. de Mathematiques et Informatique, Université de Bordeaux I, 33405, Talence, France

    J. F. Colombeau

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  1. J. F. Colombeau
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Editors and Affiliations

  1. Institute of Mathematics, Novi Sad, Yugoslavia

    Bogoljub Stanković , Endre Pap  & Stevan Pilipović ,  & 

  2. Steklov Institute of Mathematics, Moscow, USSR

    Vasilij S. Vladimirov

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© 1988 Plenum Press, New York

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Colombeau, J.F. (1988). Generalized Functions; Multiplication of Distributions; Applications to Elasticity, Elastoplasticity, Fluid Dynamics and Acoustics. In: Stanković, B., Pap, E., Pilipović, S., Vladimirov, V.S. (eds) Generalized Functions, Convergence Structures, and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1055-6_2

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  • DOI: https://doi.org/10.1007/978-1-4613-1055-6_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8312-6

  • Online ISBN: 978-1-4613-1055-6

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