On viscous limit solutions of the Riemann problem for the equations of isentropic gas dynamics in Eulerian coordinates

Journal Article · Mon Jun 30 04:00:00 EDT 2003 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2003V194N06ABEH000739; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21208322

Andreianov, B P ^[1]

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1. Laboratoire de Chimie des Materiaux et des Interfaces, UFR des Sciences et Techniques, Universite de Franche-Comte, Batiment C, Besancon Cedex (France)

For the problem {rho}{sub t}+({rho}u){sub x}=0, ({rho}u){sub t}+({rho}u{sup 2}+p({rho})){sub x}=0, ({rho},u)|{sub t=0,x<0}=({rho}{sub -},u{sub -}), ({rho},u)|{sub t=0,x>0}=({rho}{sub +},u{sub +}) one shows the existence and uniqueness of a solution obtainable as a limit as {epsilon} tends to zero of the bounded self-similar solutions of the regularized problem with additional viscosity term {epsilon}tu{sub xx}, {epsilon}>0, in the second equation. The structure of the solutions is described in detail, in particular, when they contain vacuum states.

• OSTI ID: 21208322
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 6 Vol. 194; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
EQUATIONS
ISENTROPIC PROCESSES
MATHEMATICAL SOLUTIONS
RIEMANN SHEET
VACUUM STATES