On viscous limit solutions of the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates
Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 793-811
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For the problem $\rho_t+(\rho u)_x=0$,
$(\rho u)_t+(\rho u^2+p(\rho))_x=0$,
$(\rho,u)\big|_{t=0,\,x0}=(\rho_-,u_-)$,
$(\rho,u)\big|_{t=0,\,x>0}=(\rho_+,u_+)$
one shows the existence and uniqueness of a solution obtainable as
a limit as $\varepsilon$ tends to zero
of the bounded self-similar solutions of the regularized problem
with additional viscosity term $\varepsilon tu_{xx}$, $\varepsilon>0$,
in the second equation. The structure of the solutions is described in
detail, in particular, when they contain vacuum states.
@article{SM_2003_194_6_a0,
author = {B. P. Andreianov},
title = {On viscous limit solutions of the {Riemann} problem for the equations of isentropic gas dynamics in {Eulerian} coordinates},
journal = {Sbornik. Mathematics},
pages = {793--811},
publisher = {mathdoc},
volume = {194},
number = {6},
year = {2003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a0/}
}
TY - JOUR AU - B. P. Andreianov TI - On viscous limit solutions of the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates JO - Sbornik. Mathematics PY - 2003 SP - 793 EP - 811 VL - 194 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2003_194_6_a0/ LA - en ID - SM_2003_194_6_a0 ER -
%0 Journal Article %A B. P. Andreianov %T On viscous limit solutions of the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates %J Sbornik. Mathematics %D 2003 %P 793-811 %V 194 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2003_194_6_a0/ %G en %F SM_2003_194_6_a0
B. P. Andreianov. On viscous limit solutions of the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates. Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 793-811. http://geodesic.mathdoc.fr/item/SM_2003_194_6_a0/