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Existence theory for hyperbolic systems of conservation laws with general flux-functions. (English) Zbl 1036.35130

The authors study the Cauchy problem for a strictly hyperbolic system of conservation laws \(\partial_t u+\partial_x f(u)=0\) in one space dimension with the general flux vector \(f(u)\) and develop the existence theory in the class of functions with sufficiently small total variation. This theory is based on uniform estimates for the wave curves and wave interactions, which are entirely independent on the properties of flux functions, together with a new wave interaction potential. In particular, the existence theory is applied to the \(p\)-system of gas dynamics for general pressure-laws satisfying solely the hyperbolicity condition but no convexity assumptions.

MSC:

35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
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