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The semigroup generated by 2 × 2 conservation laws

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Abstract

Consider the Cauchy problem for a strictly hyperbolic 2×2 system of conservation laws in one space dimension: {ie1-01} assuming that each characteristic field is either linearly degenerate or genuinely nonlinear. This paper develops a new algorithm, based on wave-front tracking, which yields a Cauchy sequence of approximate solutions, converging to a unique limit depending continuously on the initial data. The solutions that we obtain constitute a semigroup S, defined on a set {ie1-02} of integrable functions with small total variation. For some Lipschitz constant L, we have the estimate {ie1-03}

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Authors and Affiliations

  1. S.I.S.S.A, Via Beirut 4, 34014, Trieste, Italia

    Alberto Bressan & Rinaldo M. Colombo

  2. Department of Mathematics, Via Saldini 50, 20133, Milano, Italia

    Alberto Bressan & Rinaldo M. Colombo

Authors
  1. Alberto Bressan
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  2. Rinaldo M. Colombo
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Communicated by C. Dafermos

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Bressan, A., Colombo, R.M. The semigroup generated by 2 × 2 conservation laws. Arch. Rational Mech. Anal. 133, 1–75 (1995). https://doi.org/10.1007/BF00375350

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