Geodesic
The Riemann problem for the weakly perturbed $2\times2$ hyperbolic systems
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 194-206

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The discontinuous initial value problem for a hyperbolic system of two quasilinear equations with small perturbation is considered. The asymptotics on a small parameter of an discontinuous solution is investigated. The full asymptotic expansions are constructed, when the solution of a nonperturbed problem contains two shock waves. 
@article{ZNSL_2002_285_a13,
     author = {I. O. Rasskazov},
     title = {The {Riemann} problem for the weakly perturbed $2\times2$ hyperbolic systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {194--206},
     publisher = {mathdoc},
     volume = {285},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a13/}
}
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I. O. Rasskazov. The Riemann problem for the weakly perturbed $2\times2$ hyperbolic systems. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 194-206. http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a13/