Geodesic
Systems of quasilinear conservation laws and algorithmization of variational principles
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1586-1598

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

A previously formulated new approach to the consideration of systems of quasilinear hyperbolic equations on the basis of variational principles is described in more detail in the case of special systems of three equations. It is shown that each field of characteristics can be represented as a solution of a variational problem. Moreover, the Rankine–Hugoniot relations at the corner points of the characteristics or at the intersections of the characteristics of a single family hold automatically. In the simplest case of the Hopf equation, a numerical algorithm is constructed on the basis of a variational principle. 
@article{ZVMMF_2015_55_9_a13,
     author = {Yu. G. Rykov and O. B. Feodoritova},
     title = {Systems of quasilinear conservation laws and algorithmization of variational principles},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1586--1598},
     publisher = {mathdoc},
     volume = {55},
     number = {9},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a13/}
}
TY  - JOUR
AU  - Yu. G. Rykov
AU  - O. B. Feodoritova
TI  - Systems of quasilinear conservation laws and algorithmization of variational principles
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1586
EP  - 1598
VL  - 55
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a13/
LA  - ru
ID  - ZVMMF_2015_55_9_a13
ER  - 
%0 Journal Article
%A Yu. G. Rykov
%A O. B. Feodoritova
%T Systems of quasilinear conservation laws and algorithmization of variational principles
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1586-1598
%V 55
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a13/
%G ru
%F ZVMMF_2015_55_9_a13
Yu. G. Rykov; O. B. Feodoritova. Systems of quasilinear conservation laws and algorithmization of variational principles. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1586-1598. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a13/