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Systems of conservation laws and BV stability. (Systèmes de lois de conservation et stabilité BV.) (French) Zbl 0926.35086
The author considers global existence of the solutions to the Cauchy problem for strictly hyperbolic systems of conservation laws. In particular, he is concerned with the requirement that the total variation of initial data should be sufficiently small, and he gives certain criterion, under which this restriction may be relaxed. In this context, the variation computed on intervals of fixed (appropriate) length is decreasing. The different applications of this new notion of decrease are related to the existence in the large for periodic initial data with small BV-norm by period, to the compactness properties of the solution operator and to better life span in the case of small amplitude but large variation.
Reviewer: A.Doktor (Praha)

MSC:
35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
35B40 Asymptotic behavior of solutions to PDEs
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