The co-divergence of vector valued currents
Reuven Segev Lior Falach
Discrete & Continuous Dynamical Systems - B 2012, 17(2): 687-698 doi: 10.3934/dcdsb.2012.17.687
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: balance equations de Rham currents Continuum mechanics boundary operator vector valued currents differential operators.

Year of publication

Related Authors

Related Keywords

[Back to Top]