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TMF, 2015, Volume 185, Number 2, Pages 227–251 (Mi tmf8960)  

This article is cited in 10 scientific papers (total in 10 papers)

Conservation laws, differential identities, and constraints of partial differential equations

V. V. Zharinov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We consider specific cohomological properties such as low-dimensional conservation laws and differential identities of systems of partial differential equations (PDEs). We show that such properties are inherent to complex systems such as evolution systems with constraints. The mathematical tools used here are the algebraic analysis of PDEs and cohomologies over differential algebras and modules.

Keywords: differential algebra, conservation law, differential identity, differential constraint

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/tmf8960

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English version:
Theoretical and Mathematical Physics, 2015, 185:2, 1557–1581

Bibliographic databases:

Document Type: Article
Received: 05.05.2015

Citation: V. V. Zharinov, “Conservation laws, differential identities, and constraints of partial differential equations”, TMF, 185:2 (2015), 227–251; Theoret. and Math. Phys., 185:2 (2015), 1557–1581

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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. A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Zharinov, “Bäcklund transformations”, Theoret. and Math. Phys., 189:3 (2016), 1681–1692  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. M. O. Katanaev, “Cosmological models with homogeneous and isotropic spatial sections”, Theoret. and Math. Phys., 191:2 (2017), 661–668  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64  mathnet  crossref  crossref  isi  elib  elib
    5. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
    6. V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108  mathnet  crossref  crossref  isi  elib  elib
    7. A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271  mathnet  crossref  crossref  isi  elib  elib
    8. V. V. Zharinov, “Analysis in differential algebras and modules”, Theoret. and Math. Phys., 196:1 (2018), 939–956  mathnet  crossref  crossref  adsnasa  isi  elib
    9. N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27  mathnet  crossref  isi
    10. Katanaev M.O., “Description of Disclinations and Dislocations By the Chern-Simons Action For So(3) Connection”, Phys. Part. Nuclei, 49:5 (2018), 890–893  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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