L-P-decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity in n-dimensions

摘要

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-l.p (1 <= p <= infinity) norm for the perturbation from the planar viscous rarefaction wave. The analysis based on the new L-P-energy method and L-1-estimates. (C) 2008 Elsevier Ltd. All rights reserved.