Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the problem $\rho_t+(\rho u)_x=0$, $(\rho u)_t+(\rho u^2+p(\rho))_x=0$, $(\rho,u)\big|_{t=0,\,x<0}=(\rho_-,u_-)$, $(\rho,u)\big|_{t=0,\,x>0}=(\rho_+,u_+)$ 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. 
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     author = {B. P. Andreianov},
     title = {On viscous limit solutions of the {Riemann} problem for the equations of isentropic gas dynamics in {Eulerian} coordinates},
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     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a0/}
}
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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/

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