Geodesic
Construction of the geometrical solution in the case of a rarefaction wave
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 55-66

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We consider the Riemann problem for step-like system, which is nonstrictly hyperbolic in the sense of Petrovskii. In this paper we study the case where a solution for a strictly hyperbolic subsystem is a rarefaction wave. For the last remainig equation of the considered system we give a new definition of the solution, which we call geometrical solution. We study the construction of the geometical solution and its relation to the generalized solution. In addition, we discuss the question about physical correctness of the constructed solution. 
@article{ZNSL_2020_489_a2,
     author = {V. V. Palin},
     title = {Construction of the geometrical solution in the case of a rarefaction wave},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--66},
     publisher = {mathdoc},
     volume = {489},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a2/}
}
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V. V. Palin. Construction of the geometrical solution in the case of a rarefaction wave. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 55-66. http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a2/