Geodesic
Limit Passage in the Construction of a Geometric Solution: The Case of a Rarefaction Wave
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 182-201

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A method for constructing a geometric solution of the Riemann problem is described for a scalar conservation law perturbed by a rarefaction wave. The phase flow of the associated autonomous system is described topologically, and an explicit formula for the Hausdorff limit defining a geometric solution is presented. 
@article{TM_2021_315_a12,
     author = {V. V. Palin},
     title = {Limit {Passage} in the {Construction} of a {Geometric} {Solution:} {The} {Case} of a {Rarefaction} {Wave}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {182--201},
     publisher = {mathdoc},
     volume = {315},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_315_a12/}
}
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V. V. Palin. Limit Passage in the Construction of a Geometric Solution: The Case of a Rarefaction Wave. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 182-201. http://geodesic.mathdoc.fr/item/TM_2021_315_a12/