Geodesic
Symmetric hyperbolic equations in the nonlinear elasticity theory
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 1034-1055 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The basic results are overviewed concerning the formulation of nonlinear elasticity equations in the form of symmetric hyperbolic systems in long-time studies performed under the direction of the first author. The underlying principles developed in those studies are stated, and some inaccuracies and errors are corrected. Procedures are described for computing the coefficient matrices of the equations from a given equation of state. 
@article{ZVMMF_2008_48_6_a8,
     author = {S. K. Godunov and I. M. Peshkov},
     title = {Symmetric hyperbolic equations in the nonlinear elasticity theory},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1034--1055},
     year = {2008},
     volume = {48},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a8/}
}
TY  - JOUR
AU  - S. K. Godunov
AU  - I. M. Peshkov
TI  - Symmetric hyperbolic equations in the nonlinear elasticity theory
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 1034
EP  - 1055
VL  - 48
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a8/
LA  - ru
ID  - ZVMMF_2008_48_6_a8
ER  - 
%0 Journal Article
%A S. K. Godunov
%A I. M. Peshkov
%T Symmetric hyperbolic equations in the nonlinear elasticity theory
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 1034-1055
%V 48
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a8/
%G ru
%F ZVMMF_2008_48_6_a8
S. K. Godunov; I. M. Peshkov. Symmetric hyperbolic equations in the nonlinear elasticity theory. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 6, pp. 1034-1055. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_6_a8/

[1] Godunov S. K., “O ponyatii obobschennogo resheniya”, Dokl. AN SSSR, 134:6 (1960), 1279–1282 | MR | Zbl

[2] Godunov S. K., “Problema obobschennogo resheniya v teorii kvazilineinykh uravnenii i v gazovoi dinamike”, Uspekhi matem. nauk, 17:3(105) (1962), 147–158 | MR | Zbl

[3] Godunov S. K. et al., “Hydrodynamics effects in colliding solids”, J. Comput. Phys., 5:5 (1970), 517–539 | DOI

[4] Godunov S. K., “Simmetricheskaya forma uravnenii magnitnoi gidrodinamiki”, Chisl. metody mekhan. splosh. sredy, 3:1 (1972), 26–34, VTs SO AN SSSR, Novosibirsk

[5] Godunov S. K., Elementy mekhaniki sploshnoi sredy, Nauka, M., 1978 | MR

[6] Godunov S. K., Gordienko V. M., “Prosteishie galileevo-invariantnye i termodinamicheski soglasovannye zakony”, Prikl. mekhan. i tekhn. fiz., 43(1) (2002), 3–16 | MR | Zbl

[7] Godunov S. K., “The equation of elasticity with dissipation as a nontrivial example of thermodynamically consistent hyperbolic equations”, J. Hyperbolic Diff. Equat., 1:4 (2004), 235–249 | DOI | MR | Zbl

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

[9] Kulikovskii A. G., Sveshnikova E. I., Nelineinye volny v uprugikh sredakh, Moskovskii litsei, M., 1998, 412 pp.

[10] Kulikovskii A. G., Sveshnikova A. I., Chugainova A. P., “Nekotorye problemy nelineinoi dinamicheskoi teorii uprugosti”, Tr. Matem. in-ta RAN, 251, 2005, 173–199 | MR | Zbl

[11] Ball J. M., “Convexity conditions and existence theorems in nonlinear elasticity”, Arch. Rational Mech. and Analys., 63 (1977), 337–403 | DOI | MR | Zbl

[12] Syarle F., Matematicheskaya teoriya uprugosti, Mir, M., 1992