%0 Journal Article
%A Ye-chi LIU
%T Time Decay Rate of Solutions Toward the Viscous Shock Waves under Periodic Perturbations for the Scalar Conservation Law with Nonlinear Viscosity
%D
%R 10.1007/s10255-023-1028-9
%J 应用数学学报(英文)
%P 28-48
%V 39
%N 1
%X In this paper, it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law, with nonlinear viscosity, different far field states and periodic perturbations, not only exists globally in time, but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity. Furthermore, the decay rate is shown. The proof is given by a technical energy method.
%U https://applmath.cjoe.ac.cn/jweb_yysxxb_en/CN/10.1007/s10255-023-1028-9