Geodesic
Similar solutions existence and features for piston problem in gas dynamics
Matematičeskoe modelirovanie, Tome 5 (1993) no. 7, pp. 71-85.

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An existence of similar solutions of piston problem for gas dynamic equations is shown. A piston velosity may increase or decrease with time. Initially a gas has zero velocity and pressure, its initial density has non-uniform distribution in space. An ad hoc form of ODE describing similar solutions is used in order to prove the existence. A space-time profiles of solutions and conditions of their non-monotony are obtained. 
@article{MM_1993_5_7_a7,
     author = {M. M. Ad'yutov and Yu. A. Klokov and A. P. Mikhailov and V. V. Stepanova and A. A. Shamray},
     title = {Similar solutions existence and features for piston problem in gas dynamics},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {71--85},
     publisher = {mathdoc},
     volume = {5},
     number = {7},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1993_5_7_a7/}
}
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M. M. Ad'yutov; Yu. A. Klokov; A. P. Mikhailov; V. V. Stepanova; A. A. Shamray. Similar solutions existence and features for piston problem in gas dynamics. Matematičeskoe modelirovanie, Tome 5 (1993) no. 7, pp. 71-85. http://geodesic.mathdoc.fr/item/MM_1993_5_7_a7/