Lp -decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity in n -dimensions Original Research Article

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 W1,p(1≤p≤∞)W1,p(1≤p≤∞) norm for the perturbation from the planar viscous rarefaction wave. The analysis based on the new LpLp-energy method and L1L1-estimates.