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The semigroup generated by 2 × 2 conservation laws
 Alberto Bressan,
 Rinaldo M. Colombo
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Consider the Cauchy problem for a strictly hyperbolic 2×2 system of conservation laws in one space dimension: {ie101} assuming that each characteristic field is either linearly degenerate or genuinely nonlinear. This paper develops a new algorithm, based on wavefront 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 {ie102} of integrable functions with small total variation. For some Lipschitz constant L, we have the estimate {ie103}
Communicated by C. Dafermos
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 Title
 The semigroup generated by 2 × 2 conservation laws
 Journal

Archive for Rational Mechanics and Analysis
Volume 133, Issue 1 , pp 175
 Cover Date
 19950301
 DOI
 10.1007/BF00375350
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Alberto Bressan ^{(1)} ^{(2)}
 Rinaldo M. Colombo ^{(1)} ^{(2)}
 Author Affiliations

 1. S.I.S.S.A, Via Beirut 4, 34014, Trieste, Italia
 2. Department of Mathematics, Via Saldini 50, 20133, Milano, Italia