Geodesic
A self-similar wave problem in a~Prandtl--Reuss elastoplastic medium
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 195-205.

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We consider a self-similar piston problem in which stresses on the boundary of a half-space are changed instantaneously. The half-space is filled with a Prandtl–Reuss medium in a uniform stressed state. It is assumed that the formation of shock waves is possible in the medium. We prove the existence of a solution to the problem in the cases when two or all three stress components are changed at the initial moment. 
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     title = {A self-similar wave problem in {a~Prandtl--Reuss} elastoplastic medium},
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A. G. Kulikovskii; A. P. Chugainova. A self-similar wave problem in a~Prandtl--Reuss elastoplastic medium. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 195-205. http://geodesic.mathdoc.fr/item/TM_2016_295_a10/

[1] Kulikovskii A. G., Chugainova A. P., “Ob oprokidyvanii voln Rimana v uprugoplasticheskikh sredakh s uprochneniem”, PMM, 77:4 (2013), 486–500 | MR

[2] Kulikovskii A. G., Chugainova A. P., “Udarnye volny v uprugoplasticheskikh sredakh so strukturoi, opredelyaemoi protsessom relaksatsii napryazhenii”, Tr. MIAN, 289, 2015, 178–194 | MR | Zbl

[3] Kulikovskii A. G., Chugainova A. P., “Issledovanie razryvov v resheniyakh uravnenii uprugoplasticheskoi sredy Prandtlya–Reissa”, ZhVMiMF, 56:4 (2016), 650–663 | MR | Zbl

[4] Balashov D. B., “O prostykh volnakh uravnenii Prandtlya–Reissa”, PMM, 56:1 (1992), 124–133 | MR | Zbl

[5] Godunov S. K., Romenskii E. I., Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Ucheb. posobie dlya fiz. i mat. spets. vuzov, Univ. ser., 4, Nauch. kn., Novosibirsk, 1998

[6] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1968 | MR

[7] Ishlinskii A. Yu., Ivlev D. D., Matematicheskaya teoriya plastichnosti, Fizmatlit, M., 2001