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The semigroup generated by $$2 \times 2$$ conservation laws. (English) Zbl 0849.35068
The Cauchy problem for a strictly hyperbolic $$2\times 2$$ system of conservation laws in one space dimension is considered, assuming that each characteristic field is either linearly degenerate or genuinely nonlinear. A new algorithm is given, based on the wavefront tracking, which yields that the Cauchy sequence of approximate solutions converge to a unique limit, depending continuously on the initial data. The solutions constitute a continuous semigroup, defined on a domain $$D\subset L^1(\mathbb{R}, \mathbb{R}^2)$$.
Reviewer: S.Tersian (Russe)

##### MSC:
 35L50 Initial-boundary value problems for first-order hyperbolic systems 35L65 Hyperbolic conservation laws
##### Keywords:
viscosity method; Riemann problem; wavefront tracking
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