Preprint 2004-007

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

Abstract: We study the Cauchy problem for a strictly hyperbolic n×n system of conservation laws in one space dimension u_t+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 L¹_loc. The last section contains an application to the 3×3 system of gas dynamics.

Paper:

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Author(s):

Marta Lewicka, <lewicka@math.uchicago.edu>

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<lewicka@math.uchicago.edu> February 20 2004.