Archive for Rational Mechanics and Analysis

, Volume 133, Issue 1, pp 1–75

The semigroup generated by 2 × 2 conservation laws

  • Alberto Bressan
  • Rinaldo M. Colombo
Article

DOI: 10.1007/BF00375350

Cite this article as:
Bressan, A. & Colombo, R.M. Arch. Rational Mech. Anal. (1995) 133: 1. doi:10.1007/BF00375350

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}

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Alberto Bressan
    • 1
    • 2
  • Rinaldo M. Colombo
    • 1
    • 2
  1. 1.S.I.S.S.ATriesteItalia
  2. 2.Department of MathematicsMilanoItalia

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