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Stability of viscous shocks in isentropic gas dynamics. (English) Zbl 1171.35071

The authors consider the stability problem for viscous shock solutions of the isentropic compressible adiabatic Navier-Stokes equations in one spatial dimension. Using energy estimates, they study the spectral stability of shocks depending on their strength. Calculating numerically the Evans function and finite-difference method, the authors show that shocks are spectrally stable up to rather high values, and suggest that they are stable independently on amplitude.

MSC:

35L65 Hyperbolic conservation laws
35B35 Stability in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
35P05 General topics in linear spectral theory for PDEs
35P15 Estimates of eigenvalues in context of PDEs
76L05 Shock waves and blast waves in fluid mechanics
76N15 Gas dynamics (general theory)
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