On limits of solutions of the Riemann problem for a system of isentropic gas dynamics with viscosity in Euler coordinates. (English. Russian original) Zbl 1065.35180
Sb. Math. 194, No. 6, 793-811 (2003); translation from Mat. Sb. 194, No. 6, 3-22 (2003).
The one-dimensional Euler equations of the isentropic gas are considered with the Riemann initial data. The unique existence of a self-similar solution is proved by applying the artificial viscosity \(\varepsilon t\) to the momentum equation. With such a viscosity, the approximation system admits solutions depending on the variable \(x/t\).
Reviewer: Vladimir Shelukhin (Novosibirsk)
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35B25 | Singular perturbations in context of PDEs |
| 76N15 | Gas dynamics (general theory) |
| 35L45 | Initial value problems for first-order hyperbolic systems |
