Abstract
In this paper, we continue the scale separation approach, introduced in [S.-H. Yu, J. Amer. Math. Soc., 23 (2010), pp. 1041--1118] for the Boltzmann equation, to construct the linear wave propagation over a viscous shock profile. We have obtained exponentially sharp pointwise structure of the linear wave propagation and apply it to yield pointwise time-asymptotic convergence rate to a viscous shock profile for initial-boundary value problem.
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