Abstract
We investigate the Cauchy problem and the initial-boundary value problem for multi-dimensional conservation laws with degenerate viscosity in the whole space and in the half-space respectively. We give the optimal decay estimates in the W 1 , p ( 1 ≤ p ≤ ∞ ) norm for the perturbation from the planar viscous rarefaction wave. The analysis based on the new L p -energy method and L 1 -estimates.
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