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Well-Posedness for Hyperbolic Systems of Conservation Laws with Large BV Data

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Abstract.

We study the Cauchy problem for a strictly hyperbolic n × n system of conservation laws in one space dimension assuming that the initial data has bounded but possibly large total variation. Under a linearized stability condition on the Riemann problems generated by the jumps in 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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Authors and Affiliations

  1. University of Chicago, Department of Mathematics, Eckhart Hall, 1118 E. 58th Street, Chicago, IL 60637

    Marta Lewicka

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  1. Marta Lewicka
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Correspondence to Marta Lewicka.

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Communicated by A. Bressan

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Lewicka, M. Well-Posedness for Hyperbolic Systems of Conservation Laws with Large BV Data. Arch. Rational Mech. Anal. 173, 415–445 (2004). https://doi.org/10.1007/s00205-004-0325-6

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  • DOI: https://doi.org/10.1007/s00205-004-0325-6

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