Preprint 2004-007

On the well posedness for hyperbolic systems of conservation laws with large BV data

Marta Lewicka

Abstract: We study the Cauchy problem for a strictly hyperbolic nn system of conservation laws in one space dimension ut+f(u)x=0, assuming that the initial data u(0,x) = u0(x) has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problem generated by the jumps in u0, 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 33 system of gas dynamics.

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Marta Lewicka, <>
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<> February 20 2004.

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