Geodesic
Conservation laws, differential identities, and constraints of partial differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 227-251 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. V. Zharinov. Conservation laws, differential identities, and constraints of partial differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 2, pp. 227-251. http://geodesic.mathdoc.fr/item/TMF_2015_185_2_a0/

[1] V. V. Zharinov, TMF, 68:2 (1986), 163–171 | DOI | MR | Zbl

[2] V. V. Zharinov, Matem. sb., 181:11 (1990), 1475–1485 | DOI | MR | Zbl

[3] V. V. Zharinov, Lecture Notes on Geometrical Aspects of Partial Differential Equations, Series on Soviet and East European Mathematics, 9, World Sci., Singapore, 1992 | MR | Zbl

[4] V. V. Zharinov, Matem. sb., 184:5 (1993), 39–54 | DOI | MR | Zbl

[5] V. V. Zharinov, Tr. MIAN, 203 (1994), 478–493 | MR | Zbl

[6] V. V. Zharinov, TMF, 163:1 (2010), 3–16 | DOI | DOI | Zbl

[7] V. V. Zharinov, TMF, 174:2 (2013), 256–271 | DOI | MR | Zbl

[8] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR

[9] E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973 | MR | Zbl

[10] J. F. Ritt, Differential Algebra, Dover, New York, 1966 | MR

[11] S. Maklein, Gomologiya, Mir, M., 1966

[12] T. Tsujishita, Osaka J. Math., 19:2 (1982), 311–363 | MR | Zbl

[13] A. M. Vinogradov, I. S. Krasilschik, V. V. Lychagin, Vvedenie v geometriyu nelineinykh differentsialnykh uravnenii, Nauka, M., 1986

[14] R. Bott, L. V. Tu, Differentsialnye formy v algebraicheskoi topologii, Nauka, M., 1989 | MR