Balance Systems and the Variational Bicomplex
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 su...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147185 |
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| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725508306829312 |
|---|---|
| author | Preston, S. |
| author_facet | Preston, S. |
| citation_txt | Balance Systems and the Variational Bicomplex / S. Preston // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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].
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| first_indexed | 2025-12-07T18:52:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147185 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:52:42Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Preston, S. 2019-02-13T18:39:56Z 2019-02-13T18:39:56Z 2011 Balance Systems and the Variational Bicomplex / S. Preston // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 49Q99; 35Q80 DOI:10.3842/SIGMA.2011.063 https://nasplib.isofts.kiev.ua/handle/123456789/147185 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]. This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html.
 I would like to thank the second referee for his recommendations and comments. They allowed me to correct and/or clarify the formulations of some results and their proofs. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Balance Systems and the Variational Bicomplex Article published earlier |
| spellingShingle | Balance Systems and the Variational Bicomplex Preston, S. |
| title | Balance Systems and the Variational Bicomplex |
| title_full | Balance Systems and the Variational Bicomplex |
| title_fullStr | Balance Systems and the Variational Bicomplex |
| title_full_unstemmed | Balance Systems and the Variational Bicomplex |
| title_short | Balance Systems and the Variational Bicomplex |
| title_sort | balance systems and the variational bicomplex |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147185 |
| work_keys_str_mv | AT prestons balancesystemsandthevariationalbicomplex |