Geodesic
Evolution systems with constraints in the form of zero-divergence conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, continuity equation, conservation law, lowest-degree conservation law.
Mots-clés : constraint 
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V. V. Zharinov. Evolution systems with constraints in the form of zero-divergence conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a0/

[1] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | MR | Zbl

[2] N. Kh. Ibragimov, Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR | MR | Zbl

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

[4] I. S. Krasil'shchik, A. M. Vinogradov, Acta Appl. Math., 15:1–2 (1989), 161–209 | DOI | MR | Zbl

[5] V. V. Zharinov, Lecture Notes on Geometrical Aspects of Partial Differential Equations, Ser. Sov. East Eur. Math., 9, World Sci., Singapore, 1992 | MR | Zbl

[6] A. M. Vinogradov, I. S. Krasilschik (red.), Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki, Faktorial, M., 1997 | MR | Zbl

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

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

[9] A. M. Vinogradov, DAN SSSR, 238:5 (1978), 1028–1031 | MR | Zbl

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

[11] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Sovremennaya geometriya. Metody i prilozheniya. T. 2. Geometriya i topologiya mnogoobrazii, Editorial URSS, M., 2001 | MR | MR | Zbl

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