Transition to instability of planar viscous shock fronts: The refined stability condition
In this paper, the authors develop a simplified perturbation formula for the viscosity coefficient \(\beta\) determined by the second derivatives of the Evans function associated with the linearized operator about the shock wave, which can be applied to general shock waves. It was showed by \textit{K. Zumbrun} and \textit{D. Serre} [Indiana Univ. Math. J. 48, No.~3, 937--992 (1999; Zbl 0944.76027)] that the viscosity coefficient \(\beta\) plays an important role for the transition under localized (\(L^1\cap H^s\)) perturbations.
viscous conservation laws, spectral stability
scientific article; zbMATH DE number 5374717
scientific article