For a genuinely nonlinear hyperbolic system of conservation laws with added artificial viscosity, u, + f(u)x = euxx, we prove that traveling wave profiles for small amplitude extreme shocks (the slowest and fastest) are linearly stable to perturbations in initial data chosen from certain spaces with weighted norm; i.e., we show that the spectrum of the linearized equation lies strictly in the left-half plane, except for a simple eigenvalue at the origin (due to phase translations of the

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... . The weight ecx is used in components transverse to the profile, where, for an extreme shock, the linearized equation is dominated by unidirectional convection.