The semigroup generated by 2 × 2 conservation laws

Alberto Bressan, Rinaldo M. Colombo

Research output: Contribution to journalArticle

83 Citations (Scopus)

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 - Jan 1 1995

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Cauchy sequence
Front Tracking
Hyperbolic Systems of Conservation Laws
Total Variation
Wave Front
Conservation Laws
Lipschitz
Conservation
Cauchy Problem
Approximate Solution
Semigroup
Strictly
Linearly
Estimate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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The semigroup generated by 2 × 2 conservation laws. / Bressan, Alberto; Colombo, Rinaldo M.

In: Archive for Rational Mechanics and Analysis, Vol. 133, No. 1, 01.01.1995, p. 1-75.

Research output: Contribution to journalArticle

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