Abstract
We study the Cauchy problem for a strictly hyperbolic n × n system of conservation laws in one space dimension Open image in new window assuming that the initial data Open image in new window has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problems generated by the jumps in Open image in new window 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.
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