Spectral Stability Conditions for Shock Wave Patterns
نویسنده
چکیده
Abstract. We compare inviscid stability conditions obtained by Lewicka for large-amplitude shock wave patterns with “slow eigenvalue”, or low-frequency, stability conditions obtained by Lin and Schecter through a vanishing viscosity analysis of the Dafermos regularization. Under the structural condition that scattering coefficients for each component wave are positive, we show that BV and L inviscid stability are equivalent to respective versions of low-frequency Dafermos-regularized stability. When scattering coefficients appear with different signs, the conditions are in general distinct. We give various examples demonstrating this phenomenon and indicating the subtle role of cancellation in linearized behavior in the presence of negative scattering coefficients.
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