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

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

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Document Type: Article

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

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. V. V. Zharinov, “Bäcklund transformations”, Theoret. and Math. Phys., 189:3 (2016), 1681–1692
3. M. O. Katanaev, “Cosmological models with homogeneous and isotropic spatial sections”, Theoret. and Math. Phys., 191:2 (2017), 661–668
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
5. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133
6. V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108
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
8. V. V. Zharinov, “Analysis in differential algebras and modules”, Theoret. and Math. Phys., 196:1 (2018), 939–956
9. N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27
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
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