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TMF, 2010, Volume 163, Number 1, Pages 3–16 (Mi tmf6483)  

This article is cited in 3 scientific papers (total in 3 papers)

Evolution systems with constraints in the form of zero-divergence conditions

V. V. Zharinov

Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: We study evolution systems of partial differential equations in the presence of consistent constraints having the form of a system of continuity equations. We show that in addition to possible conservation laws of the standard degree equal to the number of spatial variables, each such system has conservation laws whose degree is one less than this number. We begin by completely describing the conservation laws and symmetries of the system of continuity equations. As an example, we calculate the second-degree conservation laws for the classical system of Maxwell's equations (the number of spatial variables is three here).

Keywords: evolution system, constraint, continuity equation, conservation law, lowest-degree conservation law

DOI: https://doi.org/10.4213/tmf6483

Full text: PDF file (470 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 163:1, 401–413

Bibliographic databases:

Document Type: Article
Received: 22.10.2009

Citation: V. V. Zharinov, “Evolution systems with constraints in the form of zero-divergence conditions”, TMF, 163:1 (2010), 3–16; Theoret. and Math. Phys., 163:1 (2010), 401–413

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Zharinov, “Conservation laws, differential identities, and constraints of partial differential equations”, Theoret. and Math. Phys., 185:2 (2015), 1557–1581  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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