Multidimensional Stability of Planar Viscous Shock Waves

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Existence and Stability of Multidimensional Shock Fronts in the Vanishing Viscosity Limit (2005, methodology): “Following [ZS], [Zu1], the uniform stability condition reads: Definition 2.”
Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems (2005, methodology): “, [GZ], [ZH], [ZS], [Z], [S], [Rou], and references therein1).”
Entropy and Global Existence for Hyperbolic Balance Laws (2004, background): “3) of physical systems (see Chapter 1 in the book), namely, it induces the desirable relaxation limit [20, 21] (at least) for smooth solutions, and it provides a proper setting for studying the existence and stability of relaxation shock profiles [23, 25, 14].”
Spectral Stability of Small Shock Waves (2002, methodology): “Since it is now known [Z] that spectral stability of viscous shock waves implies linearized and even nonlinear stability the remaining task is to develop tools to analyse the relevant eigenvalue problems.”
Basic Aspects of Hyperbolic Relaxation Systems (2001, background): “In addition, the sufficiency of the second stability condition has been discussed by Zumbrun in the parallel course notes [ 63 ] for the stability of relaxation shock profiles and the importance of the one-dimensional asymptotic stability condition has been shown by Zeng in [62].”