The semigroup generated by 2 × 2 conservation laws

Alberto Bressan, Rinaldo M. Colombo

Research output: Contribution to journalArticlepeer-review

83 Scopus citations

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}

Original languageEnglish (US)
Pages (from-to)1-75
Number of pages75
JournalArchive for Rational Mechanics and Analysis
Volume133
Issue number1
DOIs
StatePublished - Mar 1995

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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