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 [inline-graphic not available: see fulltext] assuming that the initial data [inline-graphic not available: see fulltext] has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problems generated by the jumps in [inline-graphic not available: see fulltext] we prove existence and uniqueness of a (local in time) BV solution, depending continuously on the initial data in L1loc. The last section contains an application to the 3 × 3 system of gas dynamics.