Abstract
This paper is concerned with the linearized stability of traveling wave solutions for systems of viscous hyperbolic conservation laws. The main purpose is to show that for a given traveling wave with shock profile from any characteristic family, there exists an appropriate weighted norm space such that the traveling wave is exponentially stable in this space. As a consequence, if the initial disturbance has average zero and decays exponentially fast as ¦x¦ → ∞, then the corresponding solution of the linearized equation decays to zero exponentially fast in t on any compact interval in x. The proof is given by applying an elementary weighted characteristic energy method to the integrated linearized system, based on the underlying wave structure.
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