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In this paper, we investigate the asymptotic behavior of solutions to theCauchy problem for the scalar viscous conservation law where the far fieldstates are prescribed. Especially, we deal with the case when the viscosity isof non-Newtonian type, including a pseudo-plastic case. When the correspondingRiemann problem for the hyperbolic part admits a Riemann solution whichconsists of single rarefaction wave, under a condition on nonlinearity of theviscosity, it is proved that the solution of the Cauchy problem tends towardthe rarefaction wave as time goes to infinity, without any smallnessconditions.

Global asymptotics toward rarefaction waves for solutions of the scalar conservation law with nonlinear viscosity