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

J. F. Colombeau
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J. F. Colombeau: Université de Bordeaux I, U.E.R. de Mathematiques et Informatique

A chapter in Generalized Functions, Convergence Structures, and Their Applications, 1988, pp 13-27 from Springer

Abstract: 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).

Keywords: Shock Wave; Heaviside Function; Algebraic Differential Equation; Viscous Medium; Shock Wave Solution (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-1055-6_2

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DOI: 10.1007/978-1-4613-1055-6_2

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