Geodesic
Goursat problem of the continuous conjugation of radial rectilinear motions of a~gas
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 601-606

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Gas dynamics equations have an isentropic solution describing the radial rectilinear motion of particles to the center and from the center with constant velocities. Two such solutions can be continuously conjugated if the Goursat problem is solved in a spatially similar domain with matched data on the characteristics. We prove the existence and uniqueness of a smooth solution of the Goursat problem in a small ball for a polytropic gas with exponent 5/3. 
@article{MZM_2006_79_4_a11,
     author = {S. V. Khabirov},
     title = {Goursat problem of the continuous conjugation of radial rectilinear motions of a~gas},
     journal = {Matemati\v{c}eskie zametki},
     pages = {601--606},
     publisher = {mathdoc},
     volume = {79},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a11/}
}
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S. V. Khabirov. Goursat problem of the continuous conjugation of radial rectilinear motions of a~gas. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 601-606. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a11/