The co-divergence of vector valued currents

Reuven Segev; Lior Falach

doi:10.3934/dcdsb.2012.17.687

Article Contents

2012, Volume 17, Issue 2: 687-698. Doi: 10.3934/dcdsb.2012.17.687

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The co-divergence of vector valued currents

Reuven Segev^1, and
Lior Falach^1,

1.
Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O.Box 653, Beer-Sheva, 84105

Received: June 2010

Revised: July 2011

Published: March 2012

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Abstract

In the context of stress theory of the mechanics of continuous media, a generalization of the boundary operator for de Rham currents---the co-divergence operator---is introduced. While the boundary operator of de Rham's theory applies to real valued currents, the co-divergence operator acts on vector valued currents, i.e., functionals dual to differential forms valued in a vector bundle. From the point of view of continuum mechanics, the framework presented here allows for the formulation of the principal notions of continuum mechanics on a manifold that does not have a Riemannian metric or a connection while at the same time allowing irregular bodies and velocity fields.

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Mathematics Subject Classification: 58A25, 74A10.

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References

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