Abstract: In this paper, we study the global existence of BV solutions of the initial value problem for the isentropic p-system, where the state equation of the gas is given by $P=Av^{-\gamma}$. For $\gamma>1$, the general existence result for large initial data has not been obtained. By using the Glimm scheme, Nishida, Smoller and Diperna successively obtained the global existence results for $(\gamma-1)\mbox{TV}(v_0(x),u_0(x))$ being small. In the present paper, by adopting a rescaling technique, we improve these results and obtain the global existence result under the condition that $(\gamma-1)^{\gamma+1}({\rm TV}(v_{0}(x)))^{\gamma-1}(\mbox{TV}(u_{0}(x)))^{2}$ is small, which implies that, for fixed $\gamma>1$, either $\mbox{TV}(v_{0}(x))$ or $\mbox{TV}(u_{0}(x))$ can be arbitrarily large.

Key words: conservation laws, p-system, vanishing viscosity method, BV solutions