Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 063, 18 pages      arXiv:1101.5375
Contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”

Balance Systems and the Variational Bicomplex

Serge Preston
Department of Mathematics and Statistics, Portland State University, Portland, OR, 97207-0751, USA

Received January 27, 2011, in final form June 30, 2011; Published online July 09, 2011

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].

Key words: variational bicomplex; balance equations.

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