On the 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 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 3×3 system of gas dynamics.
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- Marta Lewicka,
- Publishing information:
- Submitted by:
February 20 2004.
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