The co-divergence of vector valued currents

Pages: 687 - 698, Volume 17, Issue 2, March 2012

doi:10.3934/dcdsb.2012.17.687       Abstract        References        Full Text (347.1K)       Related Articles

Reuven Segev - Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O.Box 653, Beer-Sheva, 84105, Israel (email)
Lior Falach - Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O.Box 653, Beer-Sheva, 84105, Israel (email)

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.

Keywords:  de Rham currents, vector valued currents, boundary operator, Continuum mechanics, balance equations, differential operators.
Mathematics Subject Classification:  58A25, 74A10.

Received: June 2010;      Revised: July 2011;      Published: December 2011.

 References