Periodic solutions to p-system constructed through Glimm scheme

In this paper, we study periodic solution to p  -system via a modified Glimm scheme in BV space. We show that for the periodic initial data U0(x)∈L∞∩BVloc(R)U0(x)∈L∞∩BVloc(R), there exists an entropy solution U(x,t)U(x,t) which belongs to L∞∩BVloc(R×R+)L∞∩BVloc(R×R+). This problem has been studied by Frid [4]. By obtaining a more precise estimate on the approximate solution, we get a more general result.