Published In
Symmetry, Integrability and Geometry: Methods and Applications
Document Type
Article
Publication Date
2011
Subjects
Thermodynamics, Riemannian manifolds, Minimal submanifolds
Abstract
In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian part and a complemental "pure non-Lagrangian" balance system. In the case when derivatives of the dynamical fields do not enter the constitutive relations of the balance system, the "pure non-Lagrangian" systems coincide with the systems introduced by S. Godunov [Soviet Math. Dokl. 2 (1961), 947–948] and, later, asserted as the canonical hyperbolic form of balance systems in [Müller I., Ruggeri T., Rational extended thermodynamics, 2nd ed., Springer Tracts in Natural Philosophy, Vol. 37, Springer-Verlag, New York, 1998].
Persistent Identifier
http://archives.pdx.edu/ds/psu/13291
Citation Details
S. Preston,(2011) Variational Bicomplex and the Balance Systems. SIGMA, issue for S4 Symposium, SIGMA 7, 063.
Description
This is the publisher's final PDF © OECD, publication 2011. Originally published in Symmetry, Integrability and Geometry: Methods and Applications and can found online at: http://www.emis.de/journals/SIGMA/S4.html