Well-Posedness for Hyperbolic Systems of Conservation Laws with Large BV Data

We study the Cauchy problem for a strictly hyperbolic n×n system of conservation laws in one space dimension assuming that the initial data has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problems generated by the jumps in we prove existence and uniqueness of a (local in time) BV solution, depending continuously on the initial data in L¹_loc. The last section contains an application to the 3×3 system of gas dynamics.