Pointwise decaying rate of large perturbation around viscous shock for scalar viscous conservation law

In this paper, we consider the large perturbation around the viscous shock of the scalar conservation law with viscosity in one dimension case. We divide the time region into t ? T ₀ and t > T ₀ for a fixed constant T ₀ when applying energy method. Since T ₀ is fixed, the case t ? T ₀ is easy to deal with and when t > T ₀, from the decaying property of the solution, there is a priori estimate for the solution. Thus we can succeed to control the nonlinear term and get the pointwise estimate for the perturbation by the weighted energy method.