Geodesic
On invariant form of the mass conservation law
Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 33-40.

Voir la notice de l'article provenant de la source Math-Net.Ru

The theory of fiber bundles is used for representation of the mass conservation law in a form that is invariant under general transformations of the four space-time coordinates. А generalized formulation of the law is proposed on the base of transition to covariant differentiation. Some physical interpretations of the generalized formulation are discussed. 
@article{DVMG_2014_14_1_a2,
     author = {A. I. Gudimenko and M. A. Guzev},
     title = {On invariant form of the mass conservation law},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {33--40},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a2/}
}
TY  - JOUR
AU  - A. I. Gudimenko
AU  - M. A. Guzev
TI  - On invariant form of the mass conservation law
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2014
SP  - 33
EP  - 40
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a2/
LA  - ru
ID  - DVMG_2014_14_1_a2
ER  - 
%0 Journal Article
%A A. I. Gudimenko
%A M. A. Guzev
%T On invariant form of the mass conservation law
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2014
%P 33-40
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a2/
%G ru
%F DVMG_2014_14_1_a2
A. I. Gudimenko; M. A. Guzev. On invariant form of the mass conservation law. Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 33-40. http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a2/

[1] S. K. Godunov, E. I. Romenskii, Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Nauchnaya kniga, Novosibirsk, 1998

[2] S. P. Novikov, I. A. Taimanov, Sovremennye geometricheskie struktury i polya, MTsNMO, M, 2005

[3] M. M. Postnikov, Lektsii po geometrii. Semestr IV. Differentsialnaya geometriya. Ucheb. posobie dlya vuzov, Nauka. Gl. red. fiz.-mat. lit., M, 1988 | MR | Zbl

[4] I. Kolár, P. Michor, J. Slovák, Natural operations in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1993 | MR

[5] R. Darling, Differential Forms and Connections, Cambridge University Press, 1994 | MR | Zbl

[6] R. Palais, The geometrization of physics, National Tsing Hua University, Hsinchu, Taiwan, 1981

[7] D. Saunders, The Geometry of Jet Bundles, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[8] C. Truesdell, R. Toupin, The classical field theories. In Encyclopedia of Physics edited by S. Flugge, Springer-Verlag, Berlin, Gottingen, Heidelberg, 1960 | MR | Zbl

[9] F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, Berlin, 1983 | MR | Zbl

[10] V. L. Berdichevskii, Variatsionnye printsipy mekhaniki sploshnoi sredy, Nauka. Gl. red. fiz.-mat. lit., M, 1983 | MR