# The semigroup generated by 2 × 2 conservation laws

Article

- Accepted:

DOI: 10.1007/BF00375350

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

- 46 Citations
- 161 Downloads

## 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