Balance Systems and the Variational Bicomplex

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2011
• Автор: Preston, S.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2011
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/147185
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Balance Systems and the Variational Bicomplex / S. Preston // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ.

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].