Geodesic
Balance Systems and the Variational Bicomplex
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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].
Mots-clés : variational bicomplex; balance equations. 
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Serge Preston. Balance Systems and the Variational Bicomplex. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a62/

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