Asymptotic Stability Of Solutions To The Riemann Initial Value Perturbation Problem Of The Inhomogeneous Burgers Equation

In this paper,we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for inhomogeneous Burgers equation.We show for that a shock wave solution,after a finite time,actually consists of two periodic functions defining on either side of a shock,and this shock curve oscillates on both sides of the background shock curve.Both of perturbed shock waves and perturbed rarefaction waves tend to zero in the~?norm.